To be sure, you need to check the size and type of spare tire on your 1998 Expedition and compare it to the size and type of the spare tire from the 1996 Explorer. Look for the information stamped on the sidewall of the tire. The sizes might be slightly different (e.g., differing aspect ratios or rim diameters). Even a small difference might make it unsafe to use.
Using a mismatched spare is a temporary measure only for short distances at low speeds. It's crucial to replace the damaged tire with a properly sized and rated replacement as soon as possible.