Dear friend,
There are two ways of doing it. One on the client side and the other one is server side.
On client side, you javascript's method Onblur event of textBox and call a javascript method that gets value from one TextBox and sets the value in second one. So the code like following:
and in head section of page add:
on server side you can do it easily by adding an event handler, or by just calling post back to page on OnBlur Event by calling __doPostBack('','');
and on server side do expire.Value = DateTime.Parse(register.Value).AddDaye(30).ToShortString();
Hope this helps