Random variables cause much confusion in AP Stats.  You can find a brief overview as Number 7 on Jared Derksen's FAQ list.  For greater depth, Peter Flanagan-Hyde has a nice article at AP Central comparing algebraic variables to random variables.  You may or may not find a formal definition of "sum of two random variables" helpful.  Your students probably would not and in fact even few mathematical statistics textbooks attempt one.  Once we manage to add two random variables, we may be interested in computing the mean or variance of the sum.  See Dave Bock about that.