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If it's got the towing package, then I'm pretty sure that it's got the 3.73 rear axle ratio. 3.73s combined with 4.0 power, I'm pretty sure that it can do it, but I'd look into a transmission cooler soon if you plan on towing regularly.
How good are the brakes on that trailer? Will Uhaul even rent to you, there have been threads here saying Uhaul wouldn't rent anything to tow behind an Exploder.
I think this is risky. I wouldn't tow that much with my '98, I just don't trust the transmission and there are not enough brakes available if the trailer brakes fail. Your trailer/F 100 combo will almost, if not actually, outweigh you.
Good luck whichever way you go. I think the factory rating probably says you can do it, but then the factory put the half-arsed cam drives and troublesome 5 speeds and crap-shoot diff bearings in these too.....
I don't think I'd pull it with an explorer. The U-Haul trailer probably has hydraulic brakes which arn't as good as electrics IMO. The trailer probably wouldn't have brakes on both axles which would help in the braking department. Your probably also reaching the max for the hitch.