is there a specific equation or spread sheet to figure out the require takeoff and landing distance
yes but it's a large number of related equations ... not the simple exercise you might have imagined.
In general as Johnny-out-in-the-real-world, it is not feasible to reverse engineer the specific relationships which went into the AFM due to the modifying fudge factors used to make the theoretical equations fit the observations.
Suggestions -
(a) first, for each carpet (multivariate graph) on each chart, establish the sensible regions where the curves are continuous - by this, I mean the curves don't have any discontinuities (pointy bits)
(b) for each section read off a bunch of co-ordinates (points) along each line
(c) then, either
(i) set up a simple set of look up tables (spreadsheet is fine) to look up the values for relevant lines and then run an interpolation calculation to figure the desired intermediate point between the lines.
(ii) run a bunch of regression calculations (to figure equation representations for the lines) and then set up either interpolation or regression calculations to figure intermediate points
(d) develop this into a bigger structure to work your way through all the charts and work out the final limiting numbers.
Is this easy ? - reasonably so - but it does take a lot of careful housekeeping to keep it from going off the rails.
Once you have done all this (and you are looking at a LOT of hours work) you have the equivalent to looking up the AFM manually. The advantage is that, once done, the AFM simulation can be read in a fraction of the time it takes to use the paper copy.
Then you can use your computer simulation in the same way as the AFM for any given runway and escape terrain situation.