If Eme > -K, your utility function supports you eating meat, *regardless* of whether or not you are able to pay someone else to go veg. If Eme < -K then your utility function supports not eating meat, once again regardless of whether or not you can pay someone else to go veg. (Also you forgot a negative sign).

You wouldn't pay someone else to not eat meat unless that was the most utility generating thing you could do with your money. If your E_me > K and you would pay someone to go vegetarian, it means you are part of that "very small set" who values animals more than all other causes you might donate to while still not valuing them more than eating meat.