This is a slightly modified query from similar question:
compute sum of values associated with overlapping date ranges
SELECT "Employee_id",
SUM( "work_end_date" - "work_start_date" )
FROM(
SELECT "Employee_id",
"work_start_date" ,
lead( "work_start_date" )
over (Partition by "Employee_id"
Order by "Employee_id", "work_start_date" )
As "work_end_date"
FROM (
SELECT "Employee_id", "work_start_date"
FROM Table1
UNION
SELECT "Employee_id","work_end_date"
FROM Table1
) x
) x
WHERE EXISTS (
SELECT 1 FROM Table1 t
WHERE t."work_start_date" > x."work_end_date"
AND t."work_end_date" > x."work_start_date"
OR t."work_start_date" = x."work_start_date"
AND t."work_end_date" = x."work_end_date"
)
GROUP BY "Employee_id"
;