You have quite a fun, jaunty sort of hybrid serif/ballpoint script font there. I see what you mean about the "e". Curving the horizontal bar to form the letter into a graceful spiral is my first guess at a solution, but that might divorce it further from the design of the rest of the letters. Adding a ball terminal to either end of the stroke might resolve that.
The hook of your "t" interferes with the "m". You could try having that dip a bit below the baseline to allow some space in those close kerning situations, but then you might see problems in the "ty" combo if you take it too far.
