I don't agree with some given answers.
In russian alphabet there is two different letters: Е and Э. But in russian phonology there is only one phoneme: Э. There is no phoneme Е, it doesn't exist.
Both the letter Е and the letter Э mean the same phoneme: Э. The difference is:
(1.) Letter Э always means only phoneme Э.
(2.) And the letter Е, (2.1.) when its position in word is (2.1.1.) after vowel or (2.1.2.) in the beginning of a word, than the letter Е means two phonemes at once: ЙЭ; (2.2.) and after consonants the letter Е means that the previous consonant becomes soft and the letter Е means the phoneme Э.
Examples:
(1.) мЭр - should sound like this: hard consonant М, than vowel Э, than consonant Р — letter Е means phoneme Э
(2.1.1.) поЕхать - consonant П, vowel О, consonant Й, vowel Э, consonant Х, etc. — letter Е means phonemes Й Э
(2.1.2.) Еда - consonant Й, than vowel Э, than consonant Д, than vowel А — letter Е means phonemes Й Э
(2.2.) лЕс - Л should be soft because of Е, than vowel Э, than consonant С — letter Е makes the previous consonant Л to be soft and means phoneme Э