How about using vlookup? Do a search from comparing the larger column to the smaller and you "should" end up with 7 values (or more) as #N/A . Those values mean that they are not in that smaller list. You could also do this the other way and verify everything on the larger list is also on the smaller one. If the larger list starts at A1 and the smaller list starts at B1 then in C1 you can use the following formula.
Formula:
=if(vlookup(A1,B:B,1,false)=A1, "", "New Email")
If the email address exists in both lists, then the result will be a blank cell. If the email does not exist it will identify it with a "New Email" flag.
Then copy that formula down the C column and you will see the results. This works better than exact because using VLOOKUP doesn't require sorted information.
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