You have changed some datetime values compared to your initial post/sample. If you alter the filters to include the (startdate and) enddate, both solutions will give the correct results

--Answer 1

SELECT SUM(Boiler1) AS [OUTSIDE THE DATES 2]

FROM @Energy_Centre_Availability ECA

LEFT OUTER JOIN @Energy_Centre_Boiler_Maintenance_Schedule ECBMS

ON ECA.t_stamp >= ECBMS.StartDate

AND ECA.t_stamp <= ECBMS.EndDate

WHERE ECBMS.ndx IS NULL

--Answer 2

SELECT SUM(Boiler1) AS [OUTSIDE THE DATES 3]

FROM @Energy_Centre_Availability eca

WHERE NOT EXISTS (

SELECT 1

FROM @Energy_Centre_Boiler_Maintenance_Schedule s

WHERE eca.t_stamp >= s.startDate AND eca.t_stamp <= s.endDate

)