We are a Georgia Corporation and have hired an employee in Tennessee to do online work, how do we get a corporate tax ID # for TN withholding

After a bit of googling, I found that Tennessee doesn't have any state income tax, but they do still have unemployment. This is a link to their contact page:
Welcome - Tennessee Department of Labor and Workforce Development (http://www.tn.gov/labor-wfd/email.html)

Just call and ask. That's what I do.