Two separate updates is the simplest way:
update Employee
set EmployeeCode = 26589
where EmployeeID = 'EA45AED9-94A6-E711-AF12-E4029B75E01C' ;
update Employee
set EmployeeCode = 26587
where EmployeeID = '0A362F00-96A6-E711-AF12-E4029B75E01C';
You can wrap this in a transaction so they are effective at the same time.
You can merge them into one statement:
update Employee
set EmployeeCode = (case when EmployeeID = 'EA45AED9-94A6-E711-AF12-E4029B75E01C'26589 then 26589 else 26587 end)
where EmployeeID in ('EA45AED9-94A6-E711-AF12-E4029B75E01C', '0A362F00-96A6-E711-AF12-E4029B75E01C');
But that seems unnecessary.
If you have more than two, then this might be recommended:
update e
set EmployeeCode = v.EmployeeCode
from Employee e join
(values ('EA45AED9-94A6-E711-AF12-E4029B75E01C', 26589),
('0A362F00-96A6-E711-AF12-E4029B75E01C', 26587)
) v(EmployeeId, EmployeeCode)
on e.EmployeeId = v.EmployeeId;