If you can have macros in the files then you could do it in this basic fashion:

When a user opens a sheet, the file would have a macro that opens a simple
text file and records the user's name (from the login) and the time/date.
Obviously they could open a file without running macros and then defeat your
purpose, but you could prevent that by protecting and hiding things so that
if they open the file without the macro, the would be seeing nothing! Code
for doing that is available already by searching the programming area. If
you need help with this macro, let me know. I have some code around where I
did this previously. I got it down to tracking more than just opening, but
also what things they did when in the file. But your situation would be way
more simple.