Walking is the easiest, and fastest, way to go (I think it's more like a 5 minute walk than a 10-15 minute walk). Go to the ticket counter level and, facing the street with your back to the ticket counters, go up the escalator on the far left (there should be a sign directing you to Central Parking, and perhaps one to Terminal E). At the top of the escalator, there will be a skybridge (with moving sidewalks) to take you to the Central Parking garage. At the end of the moving walkways, keep walking straight (I suspect there will be signs directing you to Terminal E) and you will enter the skybridge that will take you directly to Terminal E.

If you're bogged down with carryons, I'd get one of those $3 carts. The MassPort bus works, too, and I think you have plenty of time (including for your checked bags), but I would walk.