ICT_SLB
As far as my memory goes, the Trident IIE was like all the other Tridents in that it had 3 Speys. It did however have some help in the in hot weather by using water injection. It also had a fin fuel tank to give it more range. It didn't have the Boost Engine though.
The IIIB was the the one with the Boost Engine (the RB162) which was needed because the poor old Speys were flat rated to 15 degrees C and needed all the help they could get