Chop down two trees, burn one to heat the other in low oxigen, this is a carbon neutral activity. Now take that biochar and bury it deep in the earth, or use it to condition the soil.
Plant two trees and let them soak up carbon.
I don't see any thermodynamic paradox there.
You could just bury trees, but I think the idea is the charcoal doesn't degrade back to carbon dioxide as quickly.