Take in both parameters as strings:
txtResult.Text = HandleInput(textbox1.Text, textbox2.Text);
public string HandleInput(string s1, string s2)
{
int i1;
int i2;
if (int.TryParse(s1, out i1) && int.TryParse(s2, out int2))
return (i1 + i2).ToString();
else
return s1 + s2;
}