Actually I am pretty sure 'any other' database, means only in Teradata.  MDIFF is a teradata specific function.  You can use the standard LAG function to do the same thing on any database which supports the SQL-99 standards.

select c1- LAG(c1,1) over (order by c2)

from <table>

That would return the current row C1 - prior row C1 (ordered by c2)

LAG(c1,2) over (order by c2) would return 2 rows prior, etc

You can also partition the data so that you only get values for a specifc data element, for example

select

     customer_id,

     purchase_amt,

     LAG(purchase_amt,1) over (partition by customer_id order by purchase_date)

from

     sales;

There are many of these analytic functions available.  SUM, AVG, COUNT, MIN, MAX, LAG, LEAD, ROW_NUMBER, RANK to name a few.  Here is a good writeup on using analytic functions in SQL.  It is written for Oracle but most of these functions will work exactly as described on pretty much any database which supports SQL-99.

http://orafaq.com/node/55

From the prior post:

select c1- LAG(c1,1) over (order by c2)

from <table>

Or in your specific case:

select promo_week_id,

          week_nbr,

          week_nbr-LAG(week_nbr,2) OVER (ORDER BY promo_week_id)

from database..table

Using SUM is interesting in a Rube Goldberg kind of way, but LAG is much easier to use for this purpose.