I had similar in not related problem with my 2004 Explorer LTD with
6-cylinder engine.

In the summer of '05 I observed a ticking sound under strong
accelaration. Truth be told I noticed this ticking sound when I first
took delivery of the car but didn't pay too much attention. This
eventually became a rough idle condition. You could feel the vibration
while holding the steering wheel. I  also noticed that the fuel
economoy began to suffer.

By early August it had become unbearable. The ticking sound became very
loud under strong acceleration and the vibration at idle was causing
the whole vehicle to unduly vibrate. The dealership changed many
sensors, cables, electronic components, and installed new engine
mounts. The dealer mechanics were stumped.

The dealership called in a roving Ford engineer who determined that the
engine had problems with internal dampners. A  new engine was ordered
and after a couple of weeks was installed. Problem solved.