RadNumericTextBox is a server-side control and it needs to be initiated on the server-side. To implement your requirement, you can use AJAX to achieve fast and instant creation of the numeric textbox dynamically. For example, you can define an asp:PlaceHolder declaratively in the mark-up of the aspx page and on a button click action create and add a RadNumericTextBox to the Controls collection of the PlaceHolder.
Alternatively, you can declare the RadNumericTextBox on the mark-up and hide it initially using its Display property. Then, you will be able to access it on the client-side and change its visibility to True using the set_visible() method.
You can also check other technology options:
Hope this helps.