Good suggestions above, but let me add a few thoughts.
First, calm down. Remind yourself it is a problem, but food aggression is normal. Your dog is not cujo, your dog is not insane, your dog is exhibiting a trait that is, well, normal. Sometimes it is overwhelming. I have seen people confused that a dog that was far from the alpha in their pack fight the alpha over food. Food is survival. The instinct to get food sometimes is hardwired in so strongly that you have dogs that may be perfectly in control in every other way, submissive, that will bite/fight for food.
In addition to working for food, crating during all meals and preferably when the other dog is visiting during even training/treat times (I frankly wouldn't give any treats while the dog is visiting), I would work on dropping treats at home and the LEAVE IT command. I would then work on doing it in public around others. I would engage people you trust to drop food. The more you can train that food is NOT his unless specifically given to HIM, the better. Is it foolproof? No. But it does help decrease it and it does usually give you a moment warning as he contemplates breaking the rule so you can stop him. And if you are going somewhere with lots of people with food, leave him home or use a basket muzzle. It is not worth the risk.