I'm not sure that I quite got there, but maybe this can give ideas.
At the outset, I'll say that it is not very efficient as it involves a crossjoin
with a data-scaffold of all dates. But this can likely be optimized, especially in Tableau Prep.
The idea is to have the start and required days in one table, the nonworking days in another,
and a scaffold of all days as a third table. The joins of this are shown in the screenshot below.
(This can be improved upon in Prep to only join those scaffold dates greater than start date).
Then there is a workingdayFlag:
IF ISNULL([Non Work]) THEN 1 ELSE 0 END
Then start adding up working days
RUNNING_SUM ( SUM ( [DayStatusFlag] ) ) - 1 // note: -1 may not be necessary
(the -1 was to match your number, but I may have it wrong as to which Friday is off)
Then the End Date is:
IF ATTR([Days Required])=[RunningSumWorkDays]
THEN ATTR([Scaffold Date])
This is all highly contingent upon the table calculation settings, screenshot below.
Finally, there are a few filters to clean things up.
Please see workbook v10.3 attached in the Forum Thread: