OKay so lets say they both break off
You have two choices:
1. Put waterpump on with two broken studs. If you go this route (I have more then once!). Use the best silicon you can find for cooling systems, make sure both surfaces are surgically clean and dry and use a thin layer of your fav silicon to sandwich the water pump gasket. Firm up the bolts nearest to the broken studs without breaking them.
Put lots of blue silicon around the broken stud area, so it fills the empty holes in the waterpump
Say a prayer that it does not leak for a long long time
2. (the better option) Remove the timing cover, plan to replace it with a new one.
By the time you remove the timing cover over both of those broken studs more times then not you will have *****ed up the cover pretty good from prying.
This is a more involved job, but one I also do alot (I specialize in 5.0's)
Ebay has a aftermarket timing cover for the explorer 5.0 for around $60-80. It works great.
You will also need a new front main seal and timing cover gasket (felpro or Ford)
a large 3 jaw puller to get the crank damper/balancer off
Oil change and fresh coolant
Permatex ultra grey
Permatex blue for cooling systems
With the timing cover off you will have a good amount of broken stud to work with to try and un thread from the block.
You will need to replace the two broken bolts, they get thread sealer on them when they go back in (Not silicon, not anti seize, thread sealer only)
You will also need to change the oil as you will get coolant in the oil pan changing the timing cover
What I do is start by draining the oil and leave the drain plug out for the whole timing cover procedure
I also use clean rags to make sure I do not get gasket material or anything else in my oil pan while it is exposed
Timing cover gasket goes on dry except for the lower oil pan part, it gets some ultra grey in the corners. as you have to cut the factory oil pan gasket a bit.