Is it possible to construct a finite state automata for a decimal adder?

Suppose the strings are of the form x#y#z , where x,y,z are strings formed from the alphabet $ \Sigma=(0,1,2,3,4,5,6,7,8,9)$ . The language is accepted if x+y=z is satisfied, for example : 56#65#121 is accepted, but 2#97#104 is not. Is it possible to find a finite automata for such a language ? I am aware of binary addition but I cannot fathom how decimal addition could be carried out using a DFA .