Engineering management is about solving problems and removing obstacles. You always have more problems than time and resources to solve them. How can you stay on top of it all?
A trick I learned from Julia Austin (my boss at Akamai some years back) was force yourself to always solve two problems at once. Before jumping on today's problem, figure out something else you can fix at the same time.
Say you have a retention problem. Engineering department scuttlebutt is that people are burned out with maintenance projects. But you are also concerned about your low bus number. I had these two problems once, and my answer was to actively shuffle engineers around onto other projects. Not quite musical chairs, but close. It worked. The engineers liked the variety, and I gave my top performers first dibs on projects, which they appreciated. There was a short-term productivity hit, but it was worth the benefits from cross-pollination and engineer happiness.
Another real-life example. I had a remote office that felt disconnected and needed some knowledge-sharing love. I had to send someone over for a few weeks. I initially planned on sending my go-to senior person, but they had had been before and to them an international trip was a chore. Instead I had an up-and-coming engineer who I wanted to invest in. This trip was a stretch for her, but I did some coaching and she did great. Plus she saw it as a perq and appreciated the responsibility.
This technique has driven a couple good behaviors for me as an engineering manager. I try to take a minute before jumping in with a solution to see what else I can do while I'm at it. It also has helped me to keep a useful (and secret) worry list and to consult it from time to time. That list is a useful way for important but not urgent problems to get mindshare. Reviewing that list became part of my Sunday evening get-ready-for-the-week routine.