The present disclosure provides substituted pyridyl-, pyrimidinyl-, pyrazinyl-, pyridazinyl-, and triazinyl-based carboxamides of Formula I-A:and the pharmaceutically acceptable salts and solvates thereof, wherein Z, HET, R10, and E are defined as set forth in the specification. The present disclosure is also directed to the use of compounds of Formula I-A to treat a disorder responsive to the blockade of sodium channels. Compounds of the present disclosure are especially useful for treating pain.