My bad, I submitted the question prematurely.
I have Outlook installed on 2 different computer (work and home) and they both connect to the same Exchange account.
I currently have Todoist Outlook installed on the Work computer and it works great. Would it be possible to install it on the home computer so that I could create a task on one and finish it up on the other?
Yes, you can log into your account from as many places as you'd like.
Well I guess it is not about the logging in part but more about making an email a task part.
If I made an email a task on one computer, would I be able to click on that task in the other computer and it would bring up the right email?
If it's both Outlook, both are signed into the same email account, it should work. If you are trying to open an Outlook email with Gmail, it's not going to.