This week's book giveaway is in the OCAJP 8 forum. We're giving away four copies of OCA Java SE 8 Programmer I Study Guide and have Edward Finegan & Robert Liguori on-line! See this thread for details.
Radio buttons are mutually exclusive, so (assuming that they are in the same group) only one can ever be checked at a time, not two. If they are not in the same group, then radio buttons don't make sense at all. Did you mean check boxes?
In any case, you can create the text fields and hide them with CSS. Upon the check box becoming checked, you use an event handler to change the CSS to make it appear.
You'll need to learn how to establish event handlers, how to modify CSS under script control, and how to use the display CSS property to show and hide elements.