Exclude members in a smart group
There's two answers, although you probably just need the first:


Instead of Advanced Search, use Search Builder (also in the Search menu).  Use "paid this year" and "email address is empty".
Alternatively, there's a custom search (Search menu > Custom Searches) called Include/Exclude by Group/Tag.  So alternatively you can create a smart group in Search Builder "No email" and combine it with existing searches using the include/exclude search.