To put a long story short there is faint white smoke coming from the back of the engine bay when I drive my car. It’s not overheating, I don’t know a lot about cars and I just recently bought this car so I was looking for help.

This is where the smoke comes from and it smells like burnt rubber kind of

 

Most likely it is from a valve cover leak causing oil to drip onto your exhaust heat shield and burn off. Mine did the same thing and went away when I replace the valve cover gasket. The VQ is notorious for leaking.

 

that would be nice if that was it. It’s just started to happen after I replaced the Variable valve time solenoid on this car. Is it bad to drive with this happening?