Use a calculated field in the where clause

This will work...

select * 
from (SELECT a, b, a+b as TOTAL FROM ( 
           select 7 as a, 8 as b FROM DUAL 
           UNION ALL 
           select 8 as a, 8 as b FROM DUAL 
           UNION ALL 
           select 0 as a, 0 as b FROM DUAL) 
    ) as Temp
WHERE TOTAL <> 0; 

Logically, the select clause is one of the last parts of a query evaluated, so the aliases and derived columns are not available. (Except to order by, which logically happens last.)

Using a derived table is away around this:

select * 
from (SELECT a, b, a+b as TOTAL FROM ( 
           select 7 as a, 8 as b FROM DUAL 
           UNION ALL 
           select 8 as a, 8 as b FROM DUAL 
           UNION ALL 
           select 0 as a, 0 as b FROM DUAL) 
    )
WHERE TOTAL <> 0 
;