Assuming you have the Ford E450 with Triton V10, I can tell you what I get with my Four Winds 28Z, which is actually 29ft-11in, so it is probably closer in size and weight to your 31E than you might first think. My rig weighs around 11,600lbs dry (probably closer to 12,900lbs when packed and occupied).
I have to tell you though, I have only had it 8 months, so I might still adjust the mileage by cross-checking the results.
The way I check mileage is with a Garmin EcoRoute HD device - it plugs into the OBDC connector on the coach, so my assumption (from again, my boating experience-I had a similar system on my boat) is that fuel flow data is transmitted to the EcoRoute.
Hooked to the EcoRoute (via Bluetooth) is a Garmin RV760LMT GPS Navigation Unit. And my second assumption is the GPS distance traveled is used along with the OBDC fuel flow data to figure out MPG. Again, that is how it worked on my boat, so I am figuring that is a pretty standard method.
So, the answer you are waiting for... I am getting just about 11MPG at 60MPH on the Freeway over flat terrain. If I get into hills, it quickly drops down to 10MPG or less. On secondary (state) highways and city driving, where there is a lot of stop/starts - I am just around 9Mpg.
I was figuring 8MPG when we bought it, so I am thrilled at 11MPG (my boat got 0.8MPG). Again though, this is only with about 400 miles with the OBDC data. I have not been able to do many "old-fashioned" comparisons (you know - fill the tank, drive x miles, fill the tank, and do the math).
I'll probably do that this summer as we get more miles on the rig as a cross-check on the OBDC data accuracy. But if indeed the fuel flow data is measured, that means things like tire size or other factors are not part of the determination. Just miles traveled per hour / gallons per hour from GPS and fuel flow data.
I have not yet towed a vehicle, but the Triton has a good reputation for producing a lot of torque... but at higher RPMs. So you may have to put your foot in it when towing in hilly terrain. Of course, that will make a lot of difference in gas mileage.
Also, you can buy the Garmin EcoRoute HD for a dozen or so different Garmin GPS units, or even if you have an Android Tablet/Smartphone - you can download the Garmin Mechanic app, which will couple to the EcoRoute and provide data. Unfortunately, there is no such app for an iPhone.