What is this smoke coming from an F/A-18 shortly before takeoff?
It is not smoke.  It is bleed air being blown behind the heat exchanger which forces cool air across the front of the heat exchanger, this is only happens on the ground. The left side of the aircraft has a secondary heat exchanger that is also cooled by a water spray nozzle.  The water is created by the ECS taking bleed air and cooling it.  The water is blown out by the bleed air so you can see it more on one side than the other. In the picture, it seems to be raining so the air being blown out is more visible because of the rainwater.
-6287 (Fixed-Wing Aircraft Safety Equipment Mechanic, F/A-18)