From everything I read on the site, TW only allows you to purchase modems that do not have the phone. To keep both, you need a splitter and two cables additional. You split the signal in and connect your old modem from TW to keep the phone and connect your new modem, then activiate it with TW, for your internet connection. I just recently did this.
TWC doesn't charge you for the phone only modem.. be sure the splitters rated for 5-1000or higher mHz and that the signal levels fall into this range: