I typically have found that many people I know of have greater success using natural supplements to help with side effects than some of the prescribed medications.
Vitamin E is a safe, natural supplement without really any side effects. It's also very difficult to overdose on it, so you can usually feel very safe taking a little more than the recommended dosage if necessary. There are very few drug interactions, and I've never read anything about Tamoxifen being a problem. However, if you're concerned about it, I would definitely talk to your doctor about it. But if he/she approves it even after your concerns, then definitely give it a try.