Took me ages to figure it out! It doesn't say in the manual. In case anyone else has wondered about it:
You do use the E key, but you need to watch your pointer. As you hover it over a movable item, the four little points move apart from each other; stab and hold the E key and the little points pinch together. Still holding down the E, move the mouse in the direction you want the item to go, and at the same time use the W, A, D, or S button to move yourself along with it. It's a bit tricky - not like in Oblivion, where it is easy-peasy - but it doesn't take long to get the hang of it. (Once you have cottoned on to it, that is!
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