SQL & PL/SQL :: Oracle - Add Numbered Column Within Query Without OVER

I am running a query in Oracle that uses multiple joins. I want to return as a part of the select statement a column that contains the row number of the result.

Here is an example of my query;

SELECT *
FROM A_TABLE
INNER JOIN THEADM.A_TABLE_EXTENSION
ON THEADM.A_TABLE_EXTENSION.OBJID = A_TABLE.OBJID
INNER JOIN THEADM.A_TABLE_ENV
ON THEADM.A_TABLE_ENV.A_TABLE_ENV2A_TABLE = A_TABLE.OBJID
INNER JOIN THEADM.A_TABLE_LOG
ON THEADM.A_TABLE_LOG.A_TABLE_LOG2A_TABLE = A_TABLE.OBJID
WHERE CREATION_TIME > '01AUG10'

I want the resulting query (after the final inner join) to contain a column named 'Column' (or similar) that contains the number of the row.

I cannot re-sort the result set - there is no criteria by which to do this. (which is why I want the row number so badly... so that I can sort the result set however I want later and return to the original using this row number) The way that it is returned from the system is the way that I need it so using OVER ORDER BY won't work for me here. I also can only read the database, I cannot INSERT or add any tables.