Is the equation the same for all data records? If so, then you can just take 19 separate entries and create a system of 19 variables and 19 equations. For example, the first equation would be:

a*18.930167 + b* 17.967469 + c* 0.008720+...+s* 972.290000 = 843.24

After you have 19 or so of those equations, you should be able to solve for a,b,c,d,...

Based on the info you provided, if you get numbers other than {1,0,-1} then you know the equation isn't the same for all entries.