How to replace cursor code with CTE in sql server 2008 - sql

Question

I have a condition where I need to pull id's from one master table and then based on that value pull values from two different tables and then update/insert into third table with these values.
I am using cursor to loop through the records in master table however I feel like this is leading to performance issue. I wanted to know if this can be done using CTE or not. I tried using CTE but it is non recursive and I am totally lost where I am going wrong.
Here is how my stored procedure is -
//
BEGIN
declare #variables char(10);
DECLARE #cursor CURSOR; --DECLARE CURSOR
SET #cursor = CURSOR FOR -- SET CURSOR
-- pull in value for curso
OPEN #cursor
FETCH NEXT
FROM #cursor INTO #variables --FILL IN CURSOR TO LOOP THROUGH
WHILE ##FETCH_STATUS = 0
BEGIN
BEGIN
--PUll values from table 1
END
BEGIN
--Pull values from table 1
-- Do some maths on the values pulled
END
BEGIN
--function/sql to update or insert
END
FETCH NEXT
FROM #cursor INTO #variables;
END
CLOSE #cursor;
DEALLOCATE #cursor;
END
//
With CTE, my code is -
//
;WITH CTE AS
(
--pull values from master table
)
BEGIN
BEGIN
-- pull values from table 1
END
BEGIN
-- Pull values from table 2, do the calculations
END
BEGIN
-- insert or update as needed.
END
//