As a Ford only guy I will agree a few of the answers above,
Change the fluid and add a friction modifier but that will only help on a limited slip and not an open diff. If that does not fix it then pull the cover and check the carrier for a bad spider gear.
those rear axles usually hold up fairly well in the Explorers so I doubt it is a broken gear.
Does it do it turning both directions left and right what speed and throttle or no throttle?