If the question means 'one other letter', I believe the answer is eye. (Adds one letter Y.)
If the question is a riddle, the answer is 'envelope' as it begins and ends with 'e', and it contains a letter.
Envelope
y
A word that begins and ends with E and has only 1 letter in between is EYE. Begins and ends with E and the Y is in between.
Tarantella is a 10 letter word. It begins with the letter T and ends with the letter A.
Envelope
Envelope begins and ends with the letter e. It contains one letter.
Quaint is a 6 letter word that begins with the letter q and ends with t.
A word that begins and ends with E and has only 1 letter in between is EYE. Begins and ends with E and the Y is in between.
Tarantella is a 10 letter word. It begins with the letter T and ends with the letter A.
E
Envelope
strengths
Excommunicate is a 13 letter word. It begins and ends with the letter e.
Envelope begins and ends with the letter e. It contains one letter.
The word is supercalifragilisticexpialidocious.
Snidely Spellbinder wrote a four-letter word that begins and ends with e. With ease.
anima asthma
* anti
Unfix is a 5 letter word. It begins with U and ends with X.