I control my T2D with diet only, and have started exercising more seriously in the last few months. I have noticed that I don't get hungry at all after workouts, even when I tried to do them fasted (I found that I couldn't lift as heavy if fasted, so I don't do that any more). My workouts used to consist of very short, intensive HIIT with kettlebells, but I phased those out when I started doing Stronglifts 5x5. Lifting heavy weights is tiring, but it doesn't provoke hunger pangs either.
I just realised it could be either the nature of the exercise (heavy lifting) or the fact that I'm keto-adapted, having been on LCHF for a long time, so my body is not craving glucose as fuel (or my liver is well-trained to provide it when needed). Maybe both.
The answer to the question what to eat before or after - I have a lunch of 500-800 cals (usually a salad with avocado and some meat/fish) about 3 hours prior to lifting then eat nothing until the next morning. My goal is to build muscle and shed about 10 kgs of fat. Oh, and I'm a middle-aged female.