For all EU V.A.T registered businesses who sell goods and services to other EU members who are also V.A.T registered should apply a 0% V.A.T at the checkout and on the invoice.
This is called intra community transaction.
Be careful, having a total exempt or with 0% V.A.T are both totally different for the government.
Now to code your logic you would need this:
When the customer checks out, his V.A.T number has to be checked against the EU database as it is now but if the V.A.T number is correct, your system should automatically apply the 0% V.A.T
It is such an important feature that I do not understand why it is not added to the WHMCS system.