_ E _ _ _ because:
1) Assume ---EP=1 then since SLEEP=1 it means SLE--=1 and since SLEPT = 2 it means --PT=1
2) Assume ---PT=1 similar to above it follows that ---EP=1
3) From #1 we have ---EP=1 <=> ---PT=1 and either of those imply SLE--=1. However if ---EP=1 and ---PT=1 then the only two possibilities are ---ET=2 or ---PP=2.
4) Assume ad absurdum ---EP=1. Then SLE--=1 as above, therefore SPE-- can be at most 2 and at worst 0 (since there is only one letter change from SLE--=1). From SPEAR=3 it follows that ---AR must be at least 1. However this contradicts both possibilities in #3 above (---ET=2 or ---PP=2). Therefore ---EP is not 1, and by #3 ---PT is not 1.
5) Assume ---EP=2 then SLE--=0 therefore ---PT=2 which is a contradiction. Similarly ---PT cannot be 2.
6) From #4 we find that ---EP=0 and ---PT=0 (not 1, not 2, cannot be greater than 2 letters). Therefore SLE--=2 from SLEEP=2.
7) SPEAR=3 so SPE-- is at least 1 since ---AR can be at most 2.
8) Assume -L---=1, then S-E--=1 from #6 and since SLABS=1 it follows that S-ABS=0 therefore --E--=1.
9) Assume -L---=0, then S-E--=2 from #6, therefore --E--=1
10) Regardless of -L--- being 1 or 0 from #8	 it follows that --E--=1
STEAM