I found a couple pages of relevance to this matter:
From that, it appears that the EU expects non-EU merchants to collect and pay VAT on export sales to individual (non-business) buyers in EU countries (EU business buyers are expected to calculate and pay their own VAT liability on import purchases); however, compliance with this is apparently voluntary, and it's not clear how they would reasonably expect to enforce non-compliance for merchants located outside EU jurisdiction. We'd recommend consulting with a qualified tax professional if you have further questions or concerns about this.
That said, if you want our cart to calculate VAT for EU buyers, just go into Seller Admin > Sales Tax/VAT, checkmark Charge VAT, and select your location as United States. Then make sure you enable Sales Tax/VAT in the settings of each product that should charge tax. You appear to have a lot of products, so if you don't already have Sales Tax/VAT enabled for them, we can enable that for all your products across the board for you; just email your request to Support along with your E-junkie account password, or your Subscription ID (from your Seller Admin > Account Summary screen), or your original activation code (from the original "Account information" email we sent you at registration).: