Without trying to examine specs online I think the answer will be no. Look at the GCVWR and see if the loaded RV with the loaded trailer will be over. I will bet it will. Then look at the GVWR. Look at the actual weight of your loaded rig and then add the tongue weight. I doubt that a properly loaded 7000# trailer will only have a tongue weight of 500#, more like 900#, but make an honest guess. Based on the year, I'll bet it will be over.
Then there is the issue of hitch and overhang. Some E350 chassis can tow that much, but they are not extended another 31" after the fact. If everything else is ok it might be worth fabrication that can make this possible.