It doesn't thread on Norm, it slips over the bezel and then fastens with set screws. I think what he needed to know is whether the bezels on the E2 and E2e are the same diameter and if the TID stops before it hits the bezel mounted clip and screw on the E2.
Actually, I think that there are two models of TID by GG&G for the Excecutive series and one fits the E2 and the other fits the E2e. You may need to make sure you get the right one, I believe the one for the E2 is a little more expensive.
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