Historical Cyrillic had no letter directly corresponding to the modern э. There were three letters instead: ѥ, е and є.
Russian recension or Church Slavonic did not use ѥ and had no phonetic distinction between е and є, they were only used to resolve homonymous singular and plural of some words: Iудєи изъ Iудеи (Jews from Judea), иду съ отцєм моимъ къ отцемъ егѡ (I go with my father to his fathers) etc. Є was also written in the beginning of words.
Russian does not contrast open and closed э. In words сэр and секс the same sound is written using different letters, in words тело and отель the different sounds are written using the same letter and there is no consensus on how to read the words like шинель and термин. There was no open э in the native Russian words at all, the sound was always yotized in the beginning of the words and after the vowels. There was a deictic particle э (similar to modern вон in вон тот) which survived in words это, эка, which in some dialects, including late Moscow, pronounced as a closed (not open) э, and that's all.
Since there was no sound to contrast, there was no letter to denote it, so Hebrew and Greek loanwords starting with ε were written using є: елей, Елеон, Европа, Ева, Есфирь, Ездра etc.
However, with development of Russian culture and science, more loanwords were introduced, and some of them, being borrowed from other languages than Byzantine Greek, required a non-yotized initial э and an open э after hard consonants (which was impossible in native Russian words). Russian speech did not accept open э after hard consonants until very recently (and does not accept it at all in some dialects even now), however, the initial non-yotized closed э was accepted right away, and a need for a letter to distinguish it from the yotized version arose. A letter for this sound, э in its modern form, was first introduced in XIV, but only made it officially to the alphabet in 1708.
So for the borrowings made in older times, like almost all biblical names and Greek names that were of interest to medieval Russian authors (Евклид, Еврипид, Евпатор), an initial е was used (for the lack of a better letter), which influenced rendition of the names by Russian readers and later became a tradition.
For the borrowings made later, when there was a letter to denote an initial non-yotized э, this letter was used.
In general, Russian language does not accept either closed or open versions for all non-yotized vowels in the beginning of the words, which results in incorrect renditions of the names borrowed from the languages which contrast open and closed vowels: Эттингер (Öttinger), Ибервег (Überweg), Юлёярви (Ylöjärvi) etc. The Russian transliterations either change the initial letter or make it yotized.
