Howling diff 04 crown vic
 

there is a noticeable howl when i let off the gas petal, what can it be and is it expensive to fix?. i am a new to the scene with my crown vic.

It could be worn pinion gear bearings..
It can be somewhat expensive since most of it will involve labor.
Two options , however, replace worn parts in differential or install a used differential from a salvage yard.

what kind of shop do such work and is it able to make a 800+ mile trip as is.?

My crystal ball is a little foggy right now, but I will say this,
It depends on just how bad the noise is now. There are folks that drive around for years with that problem and as long as lube was in there and the vehicle doesn't get pushed to the limit, they are still driving them.
Your best bet is to shop around and inquire who will take on the job. Dealerships probably will do it although switching out one differential assy and installing a replacement is no big deal. Most shops might be willing to do that.

A simple thing to check if you have the tools to do it correctly would be the pinion preload adjustment. I had a pinion nut loosen up on my 7.5" differential which gradually begun to whine.If you can't do it correctly, don't mess with it. To check and perform it correctly, you will need a dial type, 1/4 inch drive torque wrench, the correct socket w/ adaptors and 1/2 inch drive breaker bar for the pinion nut to torque only if the preload is too low. Otherwise, a noisy differential can go an awful long time before or if it will actually fail, .If it is real bad, junkyard replacement is the way to go instead of trying to rebuild your existing one.