Dozens of completely different EXP file types exist, so the only thing that is certain when it comes to tiff to exp conversion is that it is related to export of TIFF graphics files to EXP format.
One of the most likely candidates of this making embroidery designs for Melco machines (.exp) based on TIFF picture. Certainly doable, although vectors are the best source for this. But most good embroidery design tools support some kind of tracing function, so for geometric shapes and logos, this should be doable.
Updated: September 27, 2023