You must cast the content of your textbox to a DateTime. You can do this with the static method
DateTime.Parse().
DateTime date1 = DateTime.Parse(textBox1.Text);
DateTime date2 = DateTime.Parse(textBox2.Text);
TimeSpan date3 = date2 - date1;
textBox3.Text = date3.ToString();
Edit: By the time I hit Submit, Abhinav had already provided an answer.