Backwards Long Addition
Pyth, 16 bytes
Still new to Pyth, but this looks promising..
s_`smvs.[_d0lzcz

The idea here is simple. To do backwards addition, you need backwards numbers. We take the input, reverse it, make sure that it has same number of digits be adding trailing 0, sum the two numbers, reverse it again and make sure no leading zero exists.
Code expansion
              cz          # Take the input and Python split it. Splits on space automatically
    m                     # Now we map over these two strings
         _d               # Reverse the string
       .[  0lz            # Pad it with 0 on right so that its length is same as input length
     vs                   # We have array of character and number, stringify and eval
   s                      # Sum the numbers in array
  `                       # Stringify
 _                        # Reverse
s                         # Convert back to number, removing leading 0

Try it online here