The comments above are very good indeed, that is exactly what I was able to do for a long while.
I did the same thing many moons ago and recently went back to being an engineer (with great satisfaction).
The issue is: while it is relatively easy to describe what a good engineer is, in abstract, in a way that will work for most companies, it is much harder to define what a good manager should be because it all depends on the expectations (and the organization) of the company you work for.
In my case, I believe I was doing a fine job for 10-15 years of it as a manager (while still being hands-on on some aspects of the job) under the old definition, and having fun in the process, at least some of the time.
Then the company was acquired and the definition of what was a "good" manager changed. A "good" manager was not to do technical work, just to generate schedules and budgets, do personnel management (reviews, hiring), make sure processes were followed and go to meetings, lots of them, many off-site. Engineers need not apply.
These were not the favorite parts of my old job, but under the former organization, I was able to do that because it was not full time and I still had the technical side to keep me interested. However, under the new definition, I was no longer a good manager (or even an acceptable one) and I was utterly miserable. However, because I had been able to not stop being an engineer, I was still a pretty good engineer, so I was able to go back as an engineer
There are many managers meeting that description in that company and some of them do not have strong technical background and yet are apparently doing the job. It is my opinion that those that were strong technically and have been put in these positions do not enjoy their jobs very much, but it is just my opinion. I certainly did not. In many regards, I otherwise consider this company to be enlightened compared to most, they have done many of the right things for the right reasons so there is absolutely no bashing here. I just want to highlight the differences between what many perceive their job to be, and what management expects.
I was fortunate that while I was struggling as a manager under the new definition, this company developed a reasonable technical ladder as an alternative to the management ladder, so going back as an engineer had no downside on my salary or prospects.
So my recommendation is: while you should strive to do what is expected (and I cannot tell you what that is), don't completely abandon the technical aspect and let your skills go stale because if you are any good at it (and you probably are since they offered you this opportunity) that is something you can always fall back on. If you are expected to not do any technical work at all, think twice before taking the job, you probably won't be happy.
Also, in your new management responsibilities, you will have an opportunity to make sure that the company has, or develops, a technical ladder so that good engineers are not offered the choice of either becoming managers (where they may suck) or go somewhere else. That may be you :)
And one more thing: do not abandon your values. If you believe something is wrong, it is wrong. It does not matter if you wear the engineer's hat or the manager's hat. You will be the most visible technical person in the organization, that comes with responsibilities. Speak your mind in a respectful way, be yourself and represent the interests of your staff and the customers. You will be under a lot of pressure to cut corners and push your better judgement under the rug in order to meet impossible deadlines and budgets. Honestly try to make the best of it. Make friends in the management structure. You will need them one day. You were made that offer because you are smart, never forget it. You have an obligation to speak the truth.
