What is the relationship between the e value reported by HMMER and BLAST? (Are they equivalent?)
They use very different algorithms so they should not have the same E-value. BLAST uses a position-independent substitution matrix (e.g. BLOSUM) while HMMER uses a position-dependent substitution matrix that is different for every profile. Check out the "Background and Brief History" section in the HMMER's user guide. It explains the conceptual differences at a very broad level.

Therefore, I don't think there's any way to make them equivalent.