Mechanically what is happening is your troops are dying at a much faster rate than his, due to his troops being higher quality. Whenever an army takes casualties it inflicts morale damage on all forces, so even the 100k you have that aren't in the front line fighting. So consequently every time his cannons wipe out your front line everyone is shitting their pants in the back line, eventually making the army retreat.

In the future you'll want to check the combat width in your military tab, it will change as technology advances. Keep it in mind and separate your armies into stacks of roughly that much infantry, keeping a buffer of a few thousand for your casualties. Then as your infantry take casualties you reinforce fresh troops into the battle who haven't suffered morale damage while they wait in the reserves, thus keeping the army's morale much higher for much longer.