What bank angle creates the least energy loss in an emergency engine out 180 degree turn?
Asked and answered, since a any plane without a functioning engine is basicly a glider:
What is the optimal bank angle to accomplish a given turn in a glide?

Assuming the question refers to an engine failure after takeoff, there is a lot more to the stunt than just turning with the least amount of altitude loss. In any case, before attempting "the impossible turn" you must be above the safe altitude for the maneuver. If you have not yet reached safe altitude, you make an emergency landing in the front sector. The safe altitude varies heavily with different plane makes and models, but for example a C 172 needs about 500ft and rather aggressive (yet skilfull) handling according to tests made for AOPA Pilot 2002 july article.

To make an efficient 45 degree turn while maintaining a steady speed is not exctly a walk in the park if you have just lost an engine. Attempts to return to the runway after an engine failure during initial climb have a strong tendency to end in tragedy.