excel formula question with TIME

What exactly does "time before midnight" mean? I would expect that it means that the value is negative, and the default 1900 date system cannot display negative times. Some ideas for testing:

1) Format the cell as general. I would expect it to contain a negative fraction (-0.25 if the result is -6 hours, for example).
2) If the test from 1 suggests that it is just the inability of the 1900 date/time system to display negative times, then switch to the 1904 date/time system, which is not limited in this way. Be careful with this, though. As a somewhat global setting, if there are other calculations in this spreadsheet or others that depend on the 1900 date/time system, then those calculations will be thrown off.
3) If you cannot use the 1904 date/time system, then you may need to consider other approaches that either avoid the negative time, or that abandon Excel's built in date/time serial number system.

Read this if you are unfamiliar with how Excel stores dates/times: http://www.cpearson.com/Excel/datetime.htm

Perhaps use MOD, e.g.

=IF($E$2="","",MOD($E$47-TIME(0,-C15,0),1))

Just add MOD function as I suggested in my last post, in C15 copied down

=IF($C$2="","",MOD($C$24-TIME(0,-A15,0),1))