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

I have not read all the posts but:
Will 12 inch subwoofer be enough for an 18x20 room (with 10 ft cielings)
 
In short: no it will not.

Most of us has not since 1933 we know that if you want to be able to HEAR a sinus wavelength at 20Hz when you play at normal 80 db @ 1000 hz. Then you need to play the at 20 hz @ 120 db (!).

So when we study the graphs over what our ears are able to hear and at what sound pressure that is needed to have for us to be able to hear it.
https://en.m.wikipedia.org/wiki/Equal-loudness_contour

So the solution is much more cone area is needed and power. Then let a DSP mimic the courve in the link above. Then it is "enough".

I am in progress to building 2 18" that will perhaps rather close to the listening area and my miniDSP will help me. Maybe I will reach my goal. (Oh and it is OB that is another problem with that low efficiency).

My room i6 16 X 30 with an open concept like yours. I use 4 12" subwoofers. You will need at least two. With one you risk overloading it if you play stuff like pipe organs. 

I have both JL and REL in two systems.  By far the REL disappears and the bass is seamless.  That said, I have a 30x30 x9 ft room and 1 S12 greatly improved the sound paired with 802D's.  I added second S812 as a stereo pair and it resulted in another level of improvement.  I personally would either stack a second S812 or get the S212 given the size of your room.  Hope that helps.

I use an Aerial SW12 in a large room.  I will not be upgrading any time soon.  So far, very happy!

It depends on your expectations, your mains & other factors. I will describe my 2 rooms and comment on each.

Room 1, 17.5’ x 24’, the ceiling is 9’ at the sides and 14’ in the center. There is an entry to a dining room and small hall that cannot be closed off. Subwoofer is a meager 10" 50 watt. Mains have two 7" drivers each. I was quite surprised with how well the sub did in this rooms volume. I considered this sub weak in every other room I placed it in before (and with every other pair of mains). I listen to TV and 2 channel music in this room. The bass frequency is not level everywhere in the room. More importantly, I found a location for the single sub that provides good response in the two primary sitting locations, the dinner table and the couch centered in front of the TV (I can survive 5 seconds of imbalance when entering & leaving the room). I might eventually build and try out four 12" DIY subs because I already have the drivers from a previous project. I don’t feel any urgency since bass is already adequate in this scenario.

Room 2, 15’ x 22’ x 9’ ceiling (much less volume than room 1). I can close all the doors. This is the home theater room with a 12" custom built sub tuned to 20Hz. My bass expectation is higher in this room since it is 7.1 with LF effects output. The sub is excursion limited at 150-300 watts. My expectation is not met in this room so I am currently building two cabinets for 18" drivers with 32mm excursion, they will be tuned to 14Hz and leveled with a mini DSP. In this room I expect to feel the bass below 20Hz whether I can hear it or not.

Hopefully you can place your expectations and situation relative to my two examples.