'Э' often is used to transmit the sound [æ](blackpool) or diphthong [ɛə](Delaware, Blair).
There are some rules for its pronunciation:
'Э' is pronounced in initial position before hard consonants: этот, энциклопедия, эклиптика, эволюция, элементарно.
'Э' after consonants (пэр, мэр, сэр) denotes the hardness of the consonant.
'Е' reads as 'э' after some hard consonants of loanwords: фонетика, отель, кафе, эссе.
'Э' is used to write a few words of ingrained Russian: этот, этакий, это, эк, эвон, эва, эдак, эх, эхе-хе, эй, эхма, эге-ге, эге.