Simplifying Function with Recursive CTE and/or Window Function
You need an extra column to carry along the running total (fiddle).

In the recursive part of the CTE below R refers to the "previous" row and A the current one so referencing the column from R is your SUM(E1, E2, ... En-1).

WITH R
     AS (SELECT N,
                B,
                E = B,
                RunningTotalE = B
         FROM   A
         WHERE  N = 0
         UNION ALL
         SELECT A.N,
                A.B,
                E = A.B * ( 1 - R.RunningTotalE ),
                RunningTotalE = A.B * ( 1 - R.RunningTotalE ) + R.RunningTotalE
         FROM   R
                JOIN A
                  ON A.N = R.N + 1)
SELECT N,
       B,
       E = CAST(E AS DECIMAL(10,9))
FROM   R