You would need to know the exchange server's address for SMTP access. Once known, This can be achieved by connecting to the server on port 25 and using the "Date" Permanent Mail Header Field Registration keyword within the DATA (Body) of the email when composing.
telnet your.exchange.server 25
Send the following once the session is established.
Date: Sat, 21 May 2016 05:33:29 -0700
From: Tester <firstname.lastname@example.org>
Subject: Dr Who
I sent this email from the future, but wasn't sure how long it would take for you to receive it.
Source - https://tools.ietf.org/html/rfc4021
Other Source: http://www.samlogic.net/articles/smtp-commands-reference.htm
, good reference incase if anonymous smtp is not permitted as well.