Поскольку DDL еще не опубликован, это может или не может помочь.
Select e.EmployeeName,
s.SupervisorName,
es.StartDate,
es.EndDate,
EmpMaxDays.MaxDays as 'TotalNumberOfDaysAssigned'
From dbo.Employees e
Left Join dbo.EmployeeSupervisors es on es.EmployeeID = e.EmployeeId
Left Join
(
Select Max(DateDiff(day, es.StartDate, es.EndDate)) as 'MaxDays',
EmployeeId
From dbo.EmployeeSupervisor
Group By EmployeeId
)EmpMaxDays on es.EmployeeId = EmpMaxDays.EmployeeId
Left Join dbo.Supervisros s on es.SupervisorId = s.SupervisorId
Where DateDiff(day, es.StartDate, es.EndDate) = EmpMaxDays.MaxDays
And es.EmployeeId = EmpMaxDays.EmployeeId