Just for clarification can you tell us all the information you started off with? You said A+B=C+D which is one piece of information: is there any more?
Since you have four variables to start off with. it means you will need one more two get a result in two variables. Can we assume that your second result involving A-B is given?
(Sorry if it seems stupid to ask but you said assume one thing and then you state something completely different).