The main issue here is that you are using an iterative approach instead of a set-based approach.  Also, inline table valued functions are going to perform much better than scalar functions.  

I've rewritten your function as an inline table-valued function.  I also used a CTE to create a tally table on the fly.  If you already have a tally table (or Itzik Ben Gan's tally table function) you can skip the CTE.

I've also used OFFSET/FETCH to return the desired date.

CREATE FUNCTION [dbo].[fn_ADD_WORKING_DAYS] (
@DATE DATE,
@NDAYS INT 
) RETURNS TABLE WITH SCHEMABINDING
AS RETURN
WITH Tally_Base AS
(
    SELECT n
    FROM ( VALUES(0), (0), (0), (0), (0), (0), (0), (0),(0), (0) ) b(n)
)
, Tally AS
(
    SELECT ROW_NUMBER() OVER(ORDER BY @@VERSION) n
    FROM Tally_Base A
    CROSS JOIN Tally_Base B
    /* Add as many cross joins as necessary to get the maximum number of records you will need. */
)

/* If you already have a tally table in your database, you can skip the above CTE. */

SELECT dt
FROM Tally
CROSS APPLY( VALUES(DATEADD(DAY, n - 1, @Date))) dt(dt)
WHERE dt.dt NOT IN ( SELECT Dt_Holiday FROM Tbl_Holidays )
    AND DATEPART(WEEKDAY, dt) NOT IN (1, 7)
ORDER BY dt.dt
OFFSET @NDAYS - 1 ROWS
FETCH NEXT 1 ROWS ONLY

Drew