Macro to generate values until condition between 2 cell is met

Hi folks, second time I need your help. This is the last one though and the project is done
I have a cell (B18) in which a number must be entered.
That number will be used as a denominator in cells (F19:K19)
The sum of INT (F19:K19) which are in (F20:K20) must equal a predefine value set in cell E20.
I would like the user the press a macro button that will generate the proper value in cell B18 for this condition to be meet. I know that the value to be generated in B18 is in the vicinity of the value in A18.

I have join the file. Can someone help please? Thanks to the community. Very appreciated.

So your question basically boils down to this style formula (dummy values just to illustrate a point). However, I don't know how to solve for x in this situation, even though by trail and error (not algebra) I can see that one possible solution for x is x = 2.1, though there's a range of values that work.

Formula:

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So this code is... ugh. Not the real way to solve this problem, and I can't even be sure it works in all situations. Takes about 2 seconds to run, but still. Really hope somebody knows how to do this algebraically!

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