To find this information, you would need to:
1. Identify the relevant accrediting bodies: ABET (Accreditation Board for Engineering and Technology) is the primary accreditor for engineering programs in the US. You would need to check their database of accredited programs to see which offer distance learning options. This will likely involve considerable manual searching on the ABET website.
2. Check individual university websites: Even with ABET accreditation, individual universities might only offer certain engineering disciplines or specializations via distance learning. You would need to review each university's website to confirm.
Therefore, I cannot give you a precise number. It would require extensive research across many university websites and the ABET database. The number is likely in the dozens, but could be higher or lower depending on how strictly you define "distance learning" and the current accreditation status of various programs.