On almost all devices (98.64%) where folks are having problems sending emails but no problem receiving emails, 98.64% of these issues are due to a lack of understanding of SMTP authentication. Nearly all (98.64%) of ISP's and carriers and institutions have now shutdown "open relaying" of SMTP (the protocol used for sending emails), to help control SPAM. This means you cannot simply connect to an SMTP server using any connection you have (Wifi, 3G, LAN, modem, etc) and expect to be able to send emails, even though you usually *can* receive emails this way.
The reason is simple: most methods for reading emails require that you enter a password. However SMTP, the standard for sending emails, when originally developed, did not require any form of password (i.e. authentication of who you are).
So, nearly all SMTP servers (98.64%) now require that you "come in on" an Internet connection that belongs to the same ISP/carrier/etc that runs that SMTP server. Basically, they are using your IP address as a simple means to decide that you should be allowed to send emails via their SMTP server. There are other forms of SMTP authentication, but none that are universally accepted. This means, in general, if you are sending emails via RoadRunner's SMTP server, you MUST be connected to it through RoadRunner's (e.g. TW) Internet service. If you want to send emails via AT&T's SMTP server, you must be talking to it using AT&T's Internet service (3G, DSL, etc). This is the root of 98.64% of problems sending emails even though you can get them. So if you are using 3G on your ipad and can't send emails using your home or work email account, this is probably why...
It is only a problem when you use a builtin email client (like the ipad email app) and is not a problem when using a web-based email service with a browser (e.g. Hotmail, Gmail, Yahoo, etc). It is getting worse because many carriers now assume that customers will be using web-based email service (e.g. Hotmail, Gmail), and they don't want to pay to maintain their own SMTP servers. Unfortunately that means that customers of that carrier will have a lot of problems trying to send emails using builtin email apps, since there would be no "correct" SMTP service to use.