Will 12 inch subwoofer be enough for an 18x20 room (with 10 ft cielings)

I am lucky.  I have a dedicated room.  I was very impressed by room treatments improving my bass.  I have 2-10" subs.  I don't think size matters as much as being able to have multiples and treatment.  It helps every aspect of the music.  I know, this could be a moot point in your case.  So if you walk around the room and hear peaks and valleys in bass and you cant do at least one (multiple or treat) try moving sub around. 

Depends on what you listen to and how loud you listen to it.

I have a 10 x 14 x 9 room and a 4 sub dba made up of three different brands; 2-13" subs and 2-12" subs. I don't listen real loud very often but on occasion I have pushed the room to 105 db plus and in doing so I have driven one of the subs, a Rythmik F12, into thermo overload twice. Is there a problem with the Rythmik you might ask? Maybe, but Rythmik did't think so. Am I a bass head/hog? When the music calls for it; absolutely. Am I completely crazy? No question, but the moral of the story is, It depends. Know your tendencies and what you are looking for and remember, the bigger the room the harder it is to fill.

I agree that sub location is critical, but only if you have options. If you can only put the sub in one place, that is where it has to go. I have one tucked under an end table and another behind the sofa. Are these the best locations for these subs? I have no idea, these were the only places I could put them, but the room does sound better with them than without them.

is this for 2 channel or home theater? People tend to way over do bass in a 2 channel setup. I want to hear a tight every note detected bass not a muddy rattle the windows. Then with my home theater I do want to rattle the windows.

That's a good sized room.  Even if you went with a larger sub I would probably add a second one to the mix.
Depends on which sub and what type of bass you are looking for too.  Music, Home Theater, combo of both.....etc.