The recursive query you are using is correct only need to modify 2 things:

1. Join - COALESCE(e.ManagerID, e.TeamLeadID)

2. Parameter - DECLARE @EMPId INT = 1

here is the query you required:

DECLARE @EMPId INT = 1

;WITH Hierarchy AS 
(
    SELECT *  
    FROM dbo.Employee  
    WHERE employeeid = @EMPId

    UNION ALL  

    SELECT e.*
    FROM dbo.Employee e 
    INNER JOIN Hierarchy h 
        ON h.employeeid = COALESCE(e.ManagerID, e.TeamLeadID)
)  
SELECT *
FROM Hierarchy H
ORDER BY COALESCE(ManagerID, TeamLeadID)
OPTION (MAXRECURSION 1000);

this will give output as per your requirements:

1. If Employee ID = 1 ('M1')

   

2. If Employee ID = 2 ('M2')

   

3. If Employee ID = 10 ('T2_2')