E is an equational theorem prover.
CLIB is a collection of library functions for building one class of interesting and cool programs. At the moment CLIB is more suited for theorem provers and similar programs, and less useful for games. This will probably change as soon as the game potential of theorem provers is recognized. CLIB is layered, with higher layers becoming more specialized. Lower levels take care of the scientifically uninteresting, but necessary services for production-quality efficient programs, e.g. error handling, memory management, parsing of input, etc.