Hi Natalie,
Time and Expense user should be able to add a topic to an expense sheet. See link: http://screencast.com/t/fxIpYcKBiTh
T&E user should be also able to add a topic to the discussion of en expense sheet. See link: http://screencast.com/t/DzLjZqNIsR6H . Click on Add Topics and add a new topic or click on 3 dots ... to select one from your existing topics.
Can you elaborate on the issue you are facing? Is the button greyed out for the T&E user?
All the best,
Diana