SQL server create temporary function as a CTE
To replicate this kind of code, without creating a function:

CREATE FUNCTION dbo.add1(@x int)
RETURNS int
AS
BEGIN
  RETURN (SELECT @x + 1);
END
GO

SELECT dbo.add1(v.Value1), dbo.add1(v.Value2)
FROM (VALUES(1,2),(3,4)) AS v(Value1, Value2);


You can use CROSS APPLY:

SELECT z.v1, z.v2
FROM (VALUES(1,2),(3,4)) AS v(Value1, Value2)
CROSS APPLY
(
  SELECT v.Value1 + 1, v.Value2 + 1
) AS z(v1,v2);


If the function is extremely complicated and you don't want to repeat it, and that is the actual problem, you could try this solution. It is complex but allows you to only write the function once. If you need to expand this to more than two columns it gets more complicated.

CREATE TABLE #vals
(
  id int identity(1,1) primary key, 
  a  int, 
  b  int
);

INSERT #vals(a,b) VALUES(1,2),(15,16);

;WITH vals AS 
(
  SELECT * FROM #vals AS v
  UNPIVOT (Result FOR [Value] IN (a,b)) unp
  CROSS APPLY
  ( 

     /******** COMPLEX FUNCTION HERE ********/
     /**** Applies to output of unpivot *****/
     SELECT unp.Result + 10

  ) AS new(orig)
  PIVOT (MAX(orig) FOR Value IN ([a],[b])) AS p2
)
SELECT v1.id, 
  OriginalValue1 = v1.Result, 
  Value1 = v1.a, 
  OriginalValue2 = v2.Result, 
  Value2 = v2.b 
FROM vals AS v1 
JOIN vals AS v2 ON v1.id = v2.id
AND v1.a IS NOT NULL
AND v2.b IS NOT NULL;

GO
DROP TABLE #vals;


Or you could ask for the permissions to create your function somewhere.