We can sort out the climate problem with technology, sure. The thing is, we already have it.
What you probably mean is, you want to sort out the climate problem with hypothetical technology that would change absolutely nothing to our ways of life and cost us nothing. Maybe this hypothetical technology should also give us free massages otherwise who would bother changing?
There will always be a positive # of trees felled by humans. Even if there are only 10 of them on the planet.
AKA nuclear power.
Also, this only answers the question of decarbonization of the electricity, which is maybe 25% of the problem. You still need to address transportation, heating, cooling, land use, meat consumption, etc. This is where people will need to change their ways of life, at least just a bit.
Cant you already do all these with electricity?