How do I lead when I'd rather solve the problems myself?

You lead the engineering team now. You answer for the plant's performance through other people, instead of solving the problems yourself the way you used to. If you find yourself itching to just fix it, to take the problem back into your own hands, that is not a failure to adapt. It is the pull of someone who genuinely loved the solving. That itch is the crux of the hard part. You know you could crack the problem faster yourself, and instead you have to guide someone else to a solution that may be slower or different from yours. Handing over the wheel when you were the best driver is one of the most uncomfortable shifts there is. It is uncomfortable precisely because you are good. But your job changed from solving problems to building problem-solvers, and that is where your skill is needed now. Resist grabbing the wrench every time; instead, teach your people how you think, and let them struggle enough to grow. Your real output now is a team that can solve without you. Keep one meaty problem of your own to stay sharp, but let the rest be theirs. Pick one engineer to develop deeply this quarter. Leading well means multiplying your skill, not just spending it.