Having a job can at times be very exhausting. Just having the energy to do anything after 8-10 hours is something that is hard to imagine, especially those times when your body only wants is to relax on the couch.
For me the body and the brain's levels of exhaustion feels like the same, but they are indeed not. It's like when you have eaten too much for dinner, but still have room for dessert. Even though I feel like I'm tired from work, I'm actually more tired in my head, and the best cure for that is physical activity.
I know this works for me. Some times are harder than others, and those times seem to go easier by if I can work out and empty my mind now and then. I believe this is essential to keep an uncluttered mind and to fully get the most out of every day.