Why an 18" hole?
The hp required for a post hole drill varies a lot on the way the auger is built. Soil is so completely different everywhere that all a person can do is relate their own experience.
In clay, a lot depends on moisture and advancing the depth very slowly....sometimes with water.
Unfortunately, an inexpensive auger with large pitch, a simple screw tip, and a single cutting edge won't do much in heavy clay soil regardless of auger size. And an 18" would require a really big heavy tractor and probably in heavy clay a category II 3pt. And even so, that's not the way I'd go.
If you use an better auger with a fine pitch and dual cutting edges with bolt-on carbide teeth - a fairly expensive auger - then your 770 should be able to handle a 9 to 10 inch size in heavy clay if everything is right and you can advance it slow enough....maybe with some water. Not sure about an 18" on a little tractor in any soil. That's pushing things.....
Give it a try and let us know.
rScotty