cfg83:
It depends little bit how efficient your AC is... but with EER=10 rating 18000BTU unit consumes 1800W. At hot day expect little bit higher.
My rough estimate is that the PV array STC rating should be about 1.5x of your AC load power consumption. If your location is not very hot, then maybe little less. You'll also need some battery bank to "ride through" some little clouds.
Before I started buying inverters etc... I was looking for DC operated air conditioners. Some are available for trucks, but none I found suitable for household use. (And the pricing was very expensive.) The benefit of DC operated unit is that there is no need for DC/AC inverter that eats about 10% of the power! Also the DC operated AC units claim to be very efficient according to
this. You should get better than EER=15!
(Don't know at what conditions they have tested...)