Can one traveller travel with TWO tickets and a Two Together Railcard?

Unfortunately, no.

https://www.twotogether-railcard.co.uk/help/terms-conditions/

3. Both tickets must be bought together and both named cardholders must be travelling together to enable discounted tickets to be used.

However, you should be able to get a refund (perhaps with an admin fee) if you do it before when you would have travelled, or even perhaps a railcard-to-no-railcard excess, from a ticket office.

I just phoned with a person at First Transpennine Express, where I purchased the tickets.

The person on the phone advised me that, in spite of the text of the conditions of carriage, the one person still travelling should simply bring her ticket along with the railcard. Upon ticket checks, the traveller should tell the conductor that her friend could not make it. I was told that in this case, she will not be held liable to pay an excess penalty fare, as long as she can present her ticket and the railcard.