As far as I know you cannot define the PIVOT clause to use dynamic amount of columns. You need to define each returned column explicitly. So in your example the SQL should look like
SELECT * FROM (
SELECT
Employee.M_NAME AS MANAGER_NAME,
Employee.PHONE,
Employee.JOB_ID,
Employee.Assigned_DATE,
Employee.SHIFT,
Employee.Dept as Assignment,
Employee.E_ID,
Employee.NAME AS EMP_NAME,
Employee.DEPT_COLOR
FROM Employee
WHERE Assigned_Date BETWEEN TO_DATE('FD_Selected','MM/DD/YYYY')
AND TO_DATE('TD_Selected','MM/DD/YYYY')
ORDER by Employee.E_ID
) x
PIVOT (
min(Assignment)
FOR Assigned_Date IN (TO_DATE('10/10/2015', 'YYYY-MM-DD'),
TO_DATE('10/11/2015', 'YYYY-MM-DD'),
TO_DATE('10/12/2015', 'YYYY-MM-DD'),
TO_DATE('10/13/2015', 'YYYY-MM-DD'),
TO_DATE('10/14/2015', 'YYYY-MM-DD'),
TO_DATE('10/15/2015', 'YYYY-MM-DD'))
)
) p
In other words you need to build the dynamic portion when building the SQL statement itself.