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

This is an open floor plan that opens up into a very small kitchen area then narrow hallway. Will this be enough? Room layout dictates I can't have more than one sub.
One sub, ok Tekton 21" bass bin (sub) it has two M/B couplers in it to...

Great box  25 to 300 or so,, 95% + sensitive. 

In my limited (only) experience, one subwoofer added the LFE to the movies, but the low bass was localized to the left side of the room. The subwoofer was behind the left speaker. With two subwoofers, the LFE seems to come from all around the room. My vote, at least two. Some folks have recommend four.
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.

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.