Ac equipment. Minimum circuit ampacity is 18 amps max is 40. What size wire and what size breaker?

You get in trouble with inspectors and the manufacturer by exceeding the nameplate max.
You could use #10 on a 30 amp breaker unless it's a "long" run from panel.

Air conditioning equipment is sized according to Article 440 of the NEC, and this can be a very confusing Article to understand.

Don is incorrect, branch circuit sizing is not 1.25 of the nameplate rating of 40 amps.

Sizing of branch circuit conductor and circuit breaker for air conditioning or refrigeration equipment has been made less complicated by requiring manufacturers apply certain information on the nameplate to help electricians wire the unit properly.

I refer to Section 440.4 (B) of the NEC.

The two important ratings found on the nameplate is:

Minimum Branch Circuit Conductor
Maximum Overcurrent Protection Device, (or Fuse, or Inverse Time Circuit Breaker)

Fndandy listed the MCA of 18 amps.

I suspect the nameplate is being read or understood incorrectly, and that the 40 is the max rating of OCPD.

Therefore, this unit may have a #12 copper conductor as a feeder connected to a 40 Amp circuit breaker.

You may use the #10 as suggested, however the 30 amp breaker may not allow the unit to start reliably each time.