You can probably do this but it won't be simple (I don't think). You'll have to work with chunks of the string and loop through it. Also, this assumes you are only planning on displaying the result since the final answer goes into a string. Basically you are limited since there are no unsigned or 64-bit variables available on the TriPLC so you have no way of working with this data as a number.
Operand 1 is stored in A$
Operand 2 is stored in B$
Result will be stored in C$
This assumes both operands are the same length. You'll obviously need a way to deal with operands of different lengths (i.e. "1234567890" + "123")
D = 0 ' Set the carry to "0"
FOR I = LEN(A$) TO 0 STEP -1 ' Start from the end of the strings and work backwards
A = VAL(MID$(A$, I, 1))
B = VAL(MID$(B$, I, 1))
C = A + B + D
IF C > 9 THEN
D = 1 ' Carry the 1 for the next column (next iteration)
C = C - 10
ELSE
D = 0 ' Clear the carry so it won't get added in the next iteration
ENDIF
C$ = STR$(C) + C$ ' Build up the answer string
NEXT
IF D > 0 THEN ' Add the final carry if there is one
C$ = STR$(D) + C$
ENDIF
Something along those lines. I haven't tested that but I think it should get you pointed in the right direction. You can probably do other operations ( subtraction, multiplication, division) with similar loops.