Configure Outlook 2013 so that you can send email from a different email address as follows:

First make sure the From field is visible:
Click the New Email button at the top-left corner of the window.
Click the Options tab at the top of the window.
Click the From button in the Show Fields section. You should now see a From option at the top of the message section.

You can now select: "From other email address" in the From field when sending a new message. Type in the email address you want to send from!