Your plumbing should be about 50psi. The T&P valve will drip at about
150psi.
Can you see why letting it drip is a bad idea?

Someone recommended either a shock absorber or a capped pipe. The smallest
expansion tank is probably 50 times the size of a shock absorber.
Can you see why a shock absorber probably won't work?

You might want to check your water pressure. Mine is 50psi normally, and
goes up to 80psi maximum when the water heater does it worst. If yours is
enough to trip the T&P, then it might be too high to start with.