The answer is misleading because it attempts to fix a problem that is not a problem. You actually CAN have a WHERE CLAUSE in each segment of a UNION. You cannot have an ORDER BY except in the last segment. Therefore, this should work...
select top 2 t1.ID, t1.ReceivedDate
from Table t1
where t1.Type = 'TYPE_1'
-----remove this-- order by ReceivedDate desc
union
select top 2 t2.ID, t2.ReceivedDate --- add second column
from Table t2
where t2.Type = 'TYPE_2'
order by ReceivedDate desc