As far as I'm aware, you don't have to have a medical when applying for an E2 visa as it's not a residental visa. However, as Esprit has said above, you may have problems in getting medical insurance when you're in the US.

In some instances, you may be able to obtain better insurance by taking out an ex-pat policy before you leave the UK for your first two years. Various companies do these such as BUPA, PPP, IMG, etc - if you do an internet search for ex-patriate health insurance you should find some to choose from and compare.