v3.23.2

Cover	Sep. 11, 2023
Cover [Abstract]
Document Type	8-K
Amendment Flag	false
Document Period End Date	Sep. 11, 2023
Entity File Number	811-22528
Entity Registrant Name	First Trust Energy Infrastructure Fund
Entity Central Index Key	0001513789
Entity Tax Identification Number	45-2751056
Entity Incorporation, State or Country Code	MA
Entity Address, Address Line One	120 East Liberty Drive
Entity Address, Address Line Two	Suite 400
Entity Address, City or Town	Wheaton
Entity Address, State or Province	IL
Entity Address, Postal Zip Code	60187
City Area Code	630
Local Phone Number	765-8000
Written Communications	false
Soliciting Material	false
Pre-commencement Tender Offer	false
Pre-commencement Issuer Tender Offer	false
Entity Emerging Growth Company	false

Boolean flag that is true when the XBRL content amends previously-filed or accepted submission.

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No definition available.

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- Definition

Area code of city

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No definition available.

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- Definition

Cover page.

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No definition available.

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- Definition

For the EDGAR submission types of Form 8-K: the date of the report, the date of the earliest event reported; for the EDGAR submission types of Form N-1A: the filing date; for all other submission types: the end of the reporting or transition period. The format of the date is YYYY-MM-DD.

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No definition available.

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- Definition

The type of document being provided (such as 10-K, 10-Q, 485BPOS, etc). The document type is limited to the same value as the supporting SEC submission type, or the word 'Other'.

+ References

No definition available.

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Name:	dei_DocumentType
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- Definition

Address Line 1 such as Attn, Building Name, Street Name

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No definition available.

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Name:	dei_EntityAddressAddressLine1
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- Definition

Address Line 2 such as Street or Suite number

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No definition available.

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- Definition

Name of the City or Town

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No definition available.

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Balance Type:	na
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- Definition

Code for the postal or zip code

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No definition available.

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Balance Type:	na
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- Definition

Name of the state or province.

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No definition available.

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- Definition

A unique 10-digit SEC-issued value to identify entities that have filed disclosures with the SEC. It is commonly abbreviated as CIK.

+ References

Reference 1: http://www.xbrl.org/2003/role/presentationRef
-Publisher SEC
-Name Exchange Act
-Number 240
-Section 12
-Subsection b-2

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- Definition

Indicate if registrant meets the emerging growth company criteria.

+ References

Reference 1: http://www.xbrl.org/2003/role/presentationRef
-Publisher SEC
-Name Exchange Act
-Number 240
-Section 12
-Subsection b-2

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- Definition

Commission file number. The field allows up to 17 characters. The prefix may contain 1-3 digits, the sequence number may contain 1-8 digits, the optional suffix may contain 1-4 characters, and the fields are separated with a hyphen.

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No definition available.

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- Definition

Two-character EDGAR code representing the state or country of incorporation.

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No definition available.

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Data Type:	dei:edgarStateCountryItemType
Balance Type:	na
Period Type:	duration

- Definition

The exact name of the entity filing the report as specified in its charter, which is required by forms filed with the SEC.

+ References

Reference 1: http://www.xbrl.org/2003/role/presentationRef
-Publisher SEC
-Name Exchange Act
-Number 240
-Section 12
-Subsection b-2

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- Definition

The Tax Identification Number (TIN), also known as an Employer Identification Number (EIN), is a unique 9-digit value assigned by the IRS.

+ References

Reference 1: http://www.xbrl.org/2003/role/presentationRef
-Publisher SEC
-Name Exchange Act
-Number 240
-Section 12
-Subsection b-2

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Namespace Prefix:	dei_
Data Type:	dei:employerIdItemType
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- Definition

Local phone number for entity.

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No definition available.

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Name:	dei_LocalPhoneNumber
Namespace Prefix:	dei_
Data Type:	xbrli:normalizedStringItemType
Balance Type:	na
Period Type:	duration

- Definition

Boolean flag that is true when the Form 8-K filing is intended to satisfy the filing obligation of the registrant as pre-commencement communications pursuant to Rule 13e-4(c) under the Exchange Act.

+ References

Reference 1: http://www.xbrl.org/2003/role/presentationRef
-Publisher SEC
-Name Exchange Act
-Number 240
-Section 13e
-Subsection 4c

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- Definition

Boolean flag that is true when the Form 8-K filing is intended to satisfy the filing obligation of the registrant as pre-commencement communications pursuant to Rule 14d-2(b) under the Exchange Act.

+ References

Reference 1: http://www.xbrl.org/2003/role/presentationRef
-Publisher SEC
-Name Exchange Act
-Number 240
-Section 14d
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Period Type:	duration

- Definition

Boolean flag that is true when the Form 8-K filing is intended to satisfy the filing obligation of the registrant as soliciting material pursuant to Rule 14a-12 under the Exchange Act.

+ References

Reference 1: http://www.xbrl.org/2003/role/presentationRef
-Publisher SEC
-Name Exchange Act
-Section 14a
-Number 240
-Subsection 12

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Balance Type:	na
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- Definition

Boolean flag that is true when the Form 8-K filing is intended to satisfy the filing obligation of the registrant as written communications pursuant to Rule 425 under the Securities Act.

+ References

Reference 1: http://www.xbrl.org/2003/role/presentationRef
-Publisher SEC
-Name Securities Act
-Number 230
-Section 425

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FIRST TRUST ENERGY INFRASTRUCTURE FUND 8-K