I have had this question twice now over the last month, so I decided to take the time to write it up in case anyone else might need it.
While you can easily set up your Roadrunner.com email address in your iPhone, sending email is more problematical. You can send email if you are connected via WiFi, but sending mail when using the cellular data network fails. It seems your iPhone cannot connect to the outgoing email server.
When researching this problem for the first client to ask, I came across this tech note from Apple.com
iPhone: What to do if you can't send or receive Mail
This tech note gives you the steps necessary to select an outgoing email server provided by AT&T specifically for iPhone users. This outgoing mail server should work regardless of your connection to the Internet.