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Store them as character arrays (assume that the maximum number of digits is 512 or something) and use scanf to read it in. Then, align the digits and add (i.e. start summing and carrying over from the last digit).
scanf
There are libraries that handle large number arithmetic. Check out, for example, the GNU MP Bignum Library.
you might wanna explore the climits. http://www.cplusplus.com/reference/clibrary/climits/