Yes, If your time fields are properly formatted (click Format → Number → Time) you can just add and subtract times:
21:58:00 - 20:44:00 = 1:14:00
This will give you the time delta as
HH:MM:SS. And if you want to calculate the number of minutes, you can use the
Second() functions on that field:
=(Hour(D2) * 60) + Minute(D2) + (Second(D2) / 60)
Of course, if there are leap-seconds, time zone changes, or if an event takes longer than 24 hours, you will still have to adjust the results manually.
If one event stretches past midnight, say from 23:50 to 00:10, this will show up as a negative time!
In oder to have these events handled 'correctly', you can either put "24:10" or split the event into two.
A Better way
Even though it's a bit harder to input data, the most reliable way to do this is to mark the beinning and end field as "Date Time" and the delta field as "Hours", which will look like this:
Beginning End Delta
8/1/2013 0:00:00 8/2/2013 12:30:00 36:30:00