In Excel, you should have the Solver Add-In (see: this is you do not have it)
Next I created a sheet like this (using control+backquoot to show the formulas)

After make field G3 active, and click on Data/Solver via the menu.
In Dutch 'Solver' is 'Oplosser', the rest of the text in this screenshot is also in Dutch (you can say thanks to Microsoft for that! (i do not know where you can do that!))

Anyway, after entering the correct values, and hitting the 'Solve' (or 'Opslossen') button, I do get:

A correct solution to your problem is: A=4; E=4; F=16 and (B=0; C=0; D=0)
I did assume the numbers in A...F should not have decimals, be: 'geheeltallig'