I like this idea too, as it’s possibly the most clear and universal symbol for what’s happening. I think changing the color of the cursor would also be good, and it would probably be best to do both (or have options for both, at least) to bring clear attention to the changed state.
I hate to pile on, but I also don’t think an E in the middle of the brush is a good solution. Depending on the size of the brush, you might not even be able to see it, or tell what it is. And like other people mentioned, E isn’t universal, whether for the word for eraser (e.g. languages like Chinese or Japanese use symbols instead of letters), or the shortcut, which anyone can change, and might be different on different language keyboards anyway. Also, from a UX design standpoint, using letters instead of symbols is generally highly discouraged, for those same reasons. I’ve used software that had letters instead of icons on the UI buttons, and it’s terrible.
Symbols are generally much more universal to understand, and colors help distinguish changes, so in this case, my preference is to have both an eraser symbol on the bottom right of the cursor or brush outline, and a different color for the outline.