If you are at the stage of learning basic logic gates, this is what you should be thinking of:
1. adding the numbers is easy as long as they are in binary.
2. the 7 segments have to be turned on or off in combinations to make numbers appear.
So breaking your problem down, you first have two digital inputs which can carry a number in binary. Assuming you want to use at least the numbers 0 to 9, you need 4 binary inputs for each of the numbers you are going to add. So for the first input you have to convert the four bits into seven different segment signals. You have to do this again for the second four inputs so the second LED shows it's number.
Now you have two sets of 4-bit numbers and you want to show their sum, for this use a 4-bit adder circuit. The output of the adder also has to be decoded into the correct seven segment pattern so it shows on the third LED.
Hint - if you are using TTL logic, look at the data sheets for the 7447 IC which decodes 4 binary bits into the seven segment signals and look at the 74LS283 data sheet for details of a full adder IC. Even if you are not using these devices, their data sheets will help you understand the technique.
Brian.