Try switching to 1904 date system. (NT)
First, make sure the "arrival time" really is a "time" in Excel. To find out, format it as a regular number (Format -> Cells..., select the Number tab and "General" from the list of categories). It should look soomething like 35703.61667. Excel uses a serial number, starting with "1" equal to January 1, 1900 (on a PC), to represent time. If you format the above number as Time, using the format "3/4/97 13:30," you'll see it represents 10/1/01 14:48. "35703" represents the number of days since January 1, 1900 and the decimal part (.61667) is the fractional part of that day since midnight (14 hours and 48 minutes).
Assuming your voyage time of 2 hours is the number "2" and you just subtract it from the arrival time you will get a departure time that is two days earlier (rather than 2 hours). You need to divide the voyage time by 24 before subtracting it from the arrival time to get the departure time.
This may seem like it's overly complicated, but actually it is the only way to do it. For example, it needs to account for trips that start on one day and end on another.
I hope this helps.
Jay