I know how to send mail using an SMTP server specified in a mail profiler in the Database Mail of Sql Server.
You would do it like so:
EXEC msdb.dbo.sp_send_dbmail @profile_name = 'profile',
@recipients = @email,
@body = @body,
@body_format = 'HTML',
@subject = @subject
But I don't know how to send mail using Microsoft Exchange.
Update 1. I believe that the main problem of my not being able to send mail through Exchange is that it's using the NTLM-based authentication. And I most certainly don't want my Sql Server running using my domain user credentials.
Update 2. Thank you for your suggestions. Here's the catch. I don't have any control whatsoever over the corporate Exchange Server in question. So the only course of action would be to try to impersonate me on the Exchange endpoint somehow. Luckily, I can communicate with the Exchange via telnet ip-of-the-exchange-server 25.