We walk in the dark places no others will enter
We stand on the bridge and no one may pass

DECLARE @col1 VARCHAR(20), @col2 VARCHAR(20)
SELECT @col1 = '10000000', @col2 = '9870'

SELECT CAST(CAST(@col1 AS INT) + CAST(@col2 AS INT) AS VARCHAR(20))

update table
set column1 = convert(int,column1) + convert(int,column2)

UPDATE table SET
    column1 = STUFF( column1, LEN(column1) - LEN(column2) - 1,LEN(column2), column2)

;with CTE as (select * from table
where c1 like '%[0-9]%'
and c1 not like '%[a-z]%')
update cte 
set c1 = convert(int,c1)+convert(int,c2)
where c2 like '%[0-9]%'
and c2 not like '%[a-z]%'

update table
set c1 = convert(int,c1)+convert(int,c2)
where isnumeric(c1) = 1
and isnumeric(c2)= 1