I guess i have to create
- a TCP/IP packet wich encapsulate the data in the "email format" to the mail server i want to connect.
- socket
You do not need to get that 'low level' with the networking.
First try using a telnet client (on your PC) to try some of the examples given in the following links (using your target email server).
http://www.anta.net/misc/telnet-troubleshooting/smtp.shtml
http://exchange.mvps.org/smtp_frames.htm
http://support.microsoft.com/kb/153119
Once you have the hang of these examples, adapt the telnet client sketch (TelnetClient.ino) in the ethernet library examples to repeat what you have done above. (initially, you will have to use IP addresses instead or domain names unless you want to complicate things by using DNS look ups).
Then modify the sketch to do what you really want it to do.
You are only sending text strings to and fro to send a text email. If you want to send pictures/attachments, then thats another story.