Cast sender object in event handler using GetType().Name

I have an event handler for a Textbox and a RichTextBox. The code is identical, but

In handler #1 I do:

RichTextBox tb = (RichTextBox)sender

In handler #2 accordingly:

TextBox tb = (TextBox)sender

Doing so I can fully manipulate the sending control. How can I cast the sending object to Textbox or RichTextbox according to its type using

sender.GetType().Name

and then create the control at runtime and work with it? That way I only need one event handler function: less code, less errors, easier to maintain and DRY :-)