Please double check the equation you posted. I'm guessing that this is a formula you have derived from an engineering mechanics problem, that B and L are in units of length (i.e., cm), and E is Young's modulus (N/cm^2). But what is 'w'? I would thought it means either width (in cm), or perhaps force per unit length (N/cm), but in either case the units for 'f' would be a bit strange. Just wanting to make sure that are working on the correct equation.
The formula calculates the I-value for a beam within a window or door required to withstand w (windloading in Pa). f is the max deflection allowed, E- is the young modulus of the material used, L is the beam length and B is the load width.
OK, now I understand the equation a bit better. I can't vouch for its correctness, but at the least the units are consistent.
I see no way to make B the subject of the equation. However, since this is for an engineering class you should be able to use an approximation technique to calculate a value for B given values for I, w, L, E and f. You can use a technique such as Newton's method to iterate to an answer for B to whatever accuracy desired. Are you familiar with this technique? If not, see Calculus I - Newton's Method and post back with any further questions.
If you have been given values to use for I, w, L, E and f, and are trying to determine what the value of B should be that yields the correct value of I in your equation, one way to get a rough estimate for B is to plot a graph of I as a function of B. Then estimate what the value of B must be that yields the appropriate value of I. That should get you started on estimating B. Then you can iterate using values for B that deviate slightly from this first estimate to get more accuracy.