The easiest way of doing this would have a special, "secret" page (not accessible by a link from any other "public" page) on your site where the Add to Cart button has the discount code included with the button code there, so your email would simply link directly to that secret page.
To add a discount code to your Add to Cart button code, just add &discount_code=ZZZZ (where ZZZZ is your discount code) to the button URL like so:
<a href="
https://www.e-junkie.com/ecom/gb.php?c=cart&i=XXXXXX&cl=YYYYY&ejc=2&
discount_code=ZZZZ" target="ej_ejc" class="ec_ejc_thkbx" onClick="javascript:return EJEJC_lc(this);"><img src="
http://www.e-junkie.com/ej/ej_add_to_cart.gif" border="0" alt="Add to Cart"/></a>