I'd have to see a picture of the tires before I could say for sure. The Explorers I have seen with 22s have extremely small tires, and unless the Expedition was very low, I can't imagine the tires being that low profile, considering it is a full size truck. But, I will say that I would stay away from adapters. Yes, you can get an adapter to make them fit on your Ex, but they would cost nearly $300 for them. They will stick out and look out of place.
If I were you, I would just collect some more money and get some 20s.