Providing authentication details does not necessarily imply using encryption such as SSL.
So, if one cannot use the internet provider's SMTP server like A Dwarf suggested (which would actually do authentication based on the connection details, instead of login credentials), then entering some username and password without explicitely using SSL might still work very well.
(Note that a few SMTP servers only support username/password authentication when connecting through some specific port, like 587 aka Submission Identification Port, or even only on a specific domain like
authsmtp.example.com. SSL by default uses port 465, regardless of any authentication.)
Some providers also support authentication using POP before SMTP.
Though you claim you cannot install anything: if you could install DeleGate then it might be configured as a SMTP to SMTPS gateway (a bit like the question Force web address to go through https here on Super User)... So, if all else fails: what OS are you on?