i would also check the turbo to see if it shelled out and exhaust is just blowing through into the intake

 

a bent push rod is due to excessive rpm usually and will make a popping noise threw the intake. if the truck idols smooth for the most part and you are having exhaust threw the intake im going to say a burned valve which is pretty uncommon for these motors.

this guy is nuts but just check out from ~30-40 seconds and do that quick test for a bad valve
BROKEN ENGINE - YouTube!

 

and im NOT promoting bill!!! just trying to show glimmer of help! lol

 

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Ooooooooooh Steve you dun did it now you know they are gonna get you for this. Lol

 

Steve are the black SUV's outside your house yet? Lol.

 

^^^^^ Black Crown Vic, black steelie rims with tiny little hub caps, blackout grille. And an all-black E350 across the street.

 

Pushrod or valve would have been my first guess based on exhaust, but if you're just referring to smoke with no noticeable running issues, it sounds more like the CCV is disconnected under the hood.

Was the air intake removed and re-installed prior to this starting?

 

do the sides of the E350s say "Flowers By Irene" or "Carpet Installation Associates"

 

I agree with this... I bet it is just crank case gasses...