Anna had to sign off for a while, so she asked me to keep an Eye out for your reply.
For two sliders you should have a minimum 55 gallon aquarium. The lighting should be two lights one for heat and the other a UVB light to help metabolize calcium in the bodies to help prevent Metabolic Bone Disease. The diet should consist of 50% Leafy greens like collards, mustards, endives, escarole, no spinach(binds calcium). 25% of the diet can be Pellets and 25% live prey or meat items. You need a good filter system. They should be getting calcium at least 3 times a week. The problem with your turtle is a bacterial infection and will need to be treated by a Herp Vet., ASAP. Until you can get the turtle into the Vet. you can soak the turtle in a Betadine soak which will help what is going on with the skin, let the Betadine dry and then replace in the tank. I am going to give you a link about the Red eared slider turtles. I can locate a Herp Vet with a city and state. Joan
The problem is with a combination of diet and Husbandry. If the diet and husbandry is not right the animals will get sick over a period of time. If you read the Link I supplied it gives a full accounting for husbandry, diet and all Red eared slider care. Joan