Try using this formula:
=SUM(IF(FREQUENCY(IF($A$2:$A$9="1",IF($B$2:$B$9="W",IF(COUNTIFS($A$2:$A$9,1,$B$2:$B$9,"E",$C$2:$C$9,$C$2:$C$9)=0,MATCH($C$2:$C$9,$C$2:$C$9,0)))),ROW($C$2:$C$9)-ROW($C$2)+1),1))
also using CTRL+SHIFT+ENTER
The additional COUNTIFS
function gives you the extra functionality you need because that checks if there are additional rows with "E" against the relevant column C values
...or an alternative approach would be to count all different values from column C (assuming 1 in column A), and just subtract your "Count for E", so if that "Count for E" formula is in B12
use this array formula
=SUM(IF(FREQUENCY(IF($A$2:$A$9="1",MATCH($C$2:$C$9,$C$2:$C$9,0)),ROW($C$2:$C$9)-ROW($C$2)+1),1))-B12