18hp twin cylinder Briggs & Stratton backfire

timing issue. Remove the flywheel to see if it has "spun" from the keyway. If the motor doesnt run at all but just backfires thru the carb, it could also mean really bad intake valves, but I would definitely check the timing first

The timing is fixed, if you suspect the timing is off the only adjustments available are the .030 clearance from pickup to flywheel and the shear Key that positions the flywheel on the crankshaft. You would also want to make sure your valve clearance is .030 as well, the issue sounds like a valve leaking, a dead cylinder or mal adjusted valve clearance causing the exhaust valve to hang open just a bit.

check intake valves for proper seating. If the valves do not close completely it will allow the engine to backfire thru the carb. Another possibility is internal timing caused by the misalignment of the timing gears between the crankshaft and cam gears.

i have a 18hp briggs and stratton opposed twin, it is hard to start and backfires through the carb

timing key under flywheel costs 1 dollar

You may get lucky and have a sheared keyway on the flywheel . Just a lil off can make a big difference on timing.

back pressure is from a blocked muffler ( carbon build up)
if it is that old then it could be overheating from grass and dirt build up around the cylinder fins and not cooling properly

need carb kit with nedle and seat

(1)You high speed carburetor jet is too lean (2) a dirty carburetor that needs cleaning (3) dirty air filter.

Try pulling out the choke a little, if it stops backfiring the mixture is too lean, check the intake
pipes at the cyl head and also the plastic runners to the carb for leaks.
Dennis in Chicago