Why addition algorithm is not pseudo- polynomial? There is something I don't understand. 

In the Subset Sum problem, in the Dynamic Programming solution, because of  binary representation of the sum T, we say it is pseudo-polynomial in run time; we must sum in the worst case from 1 to T.

So I don't understand why the Addition algorithm is not pseudo-polynomial, when we can add great numbers too.
The reason is that the runtime of addition is proportional to the number of digits, not the value of the numbers, as it is for subset sum. Remember that the number of digits is the size of the input.