What have you tried? What are your ideas about the problem? It doesn't matter if you don't have a full attempt: any attempt and ideas are good.
A slightly more intuitive way is treat the variables as indepdenent dice rolls and since you want to find the expectation of the sum, you are finding E[Sum] = E[X1] + E[X2] + E[X3] + ... + E[X10] where all the X's have the same distribution for one dice roll.
So given this hint, can you figure out the E[Sum] if you know what the X's are (the distribution of 1 dice roll) and it's given expectation?