So I just picked up a 97 F350 7.5L gasser, dump body. What I have found for specs is:
GVWR: 11,000 Lbs
GCWR: 16,000 Lbs
Towing capacity: 7,300 Lbs

So the towing capacity is:
16,000 Lbs - Truck Wt (which cannot exceed 11,000 Lbs) = Towing Wt (which cannot exceed 7,300 Lbs)

Both the 16,000 Lbs and 7,300 Lbs limits seem low to me, have I got the #'s correct?

 

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Where did you get the Gross weight ratings from? The owners manual is where they are usually found and tow ratings are based on the powertrain combo.. engine, trans, and axle ratio. Manual transmissions are rated quite a bit lower than automatics too.

 

Truck did not come with an owners manual, it's an auto trans...I ran the VIN, maybe I am not reading the Tech Specs tab correctly?
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You need to figure out what axle ratio it has, there is an axle code on the decal on the drivers door pillar? You will notice there are a range of numbers next to GCWR, those numbers correspond to the axle ratio.. higher ratio getting a higher tow rating. If your truck has one of the superduty ratios which is very likely it could have a tow rating as high as 20k with a gross combined rating as high as 26k. I'm getting these numbers from an owners manual BTW.