You will need to have the registered mobile number with to retrieve the email address.
Go to the webmail.RoadRunner.com in the URL section of the Web Browser.
Click on the forget email address button on your screen.
Once done with the above steps, you will be asked to enter the registered mobile number.
After entering and submitting the mobile number, you will need to answer the security question. (Use the exact same alphabets to answer the question)
Your Email Address will appear on your screen.
Now if you know the password then you can sign in to the RoadRunner Email Account.

twc email login | Time Warner cable email login | Roadrunner Webmail