Three possibilities spring to mind - iridovirus, burning, lymphocystis.
Could he have burned himself on the heater? The sudden appearance does suggest a burn.
Was there any sign of anything before the sore appeared? Anything like a tiny pimple or raised scale?
Iridovirus is a distinct possibility as a lot dwarf gouramis bred in the far east are already affected by the time they arrive at the shop. But other symptoms of this disease include listlessness and colour change - he doesn't appear to have turned greyish and he looks quite perky in the photo. I would also expect a sore like that to develop from a small spot not just appear at that size.
Lymphocystis is the other thing that came to mind because I once had a betta with this disease. But in his case, it started with a raised scale which grew into a lump and took a couple of weeks to develop to the stage that looked like your gourami.
If it is a burn, he just needs lots of clean water. If it is iridovirus or lymphocysts (also viral) they are incurable. The female gourami is at risk if it is iridivirus and all the fish in the tank are at risk if it is lymphocystis.
If this was my fish I would set up a hospital tank for the gourami. Even a plastic storage box would work. He needs a filter and heater - steal some media from the current tank. Lots of live plants, even just a bunch of elodea, will help keep his water conditions good. Then change 50% of the water daily and watch him. And use separate cleaning equipment from the main tank, just in case of infection.
If it is one of the viruses, this will stop it passing to the other fish. Lymphocystis only passes on spores when the lump bursts open so if it does turn out to be this the other fish won't be infected yet. If it is a burn, it will give it chance to heal without the risk of the other fish picking at the sore.
With a burn, there is a chance that it could become infected. If you do set up a hospital tank it could be worth also treating with eSHa 2000 as a preventative. But don't use this in the main tank as all medication affects fish and you don't need to treat the other healthy fish.