Your T-amp (or at least all of the T-amps I've seen) doesn't have balanced inputs, only unbalanced. The breakout cable supplied with your Duet has unbalanced 1/4" outputs, and should have included 1/4" to RCA adapters so that you can use a standard pair of RCA audio cables.
If you wanted to eliminate that extra 1/4" to RCA adapter, you could source cables that have a 1/4" plug on one end and an RCA plug on the other.
Steve