We don't need both. Both would just make it easier.
What we don't have is time. Nuclear is slow to bring online, and we've lost a lot of the expertise associated with it. We don't have 20 years to retrain the personnel, educate the public, and get the designs done and built, at scale. Solar and other renewables are ready to go now.
The only weakness is energy storage/buffering. That can be covered by either additional storage, or over supply, combined with supplementary usage, like desalination, or hydrogen/hydrocarbon production.
Don't get me wrong, nuclear should be part of the solution, but we no longer have time to wait on it anymore.