Generate a "multi variable non linear equation" from a "data set" is called Curve Fitting Method. There are large number of software, witch can solve curve fitting problem like Matlab (With Curve Fitting Toolbox), Python (With Scipy Package), Excel, SPSS etc.

Below links may helpful for you:

https://en.wikipedia.org/wiki/Curve_fitting

https://www.youtube.com/watch?v=bSmbaOVKeaU

https://www.youtube.com/watch?v=LxcH9hRmxCs

https://www.youtube.com/watch?v=OmeQBaJP2e4

thanks monjur, but, I need to have an elaborate mathematical tools or methods....even supported by software. Yes, equation with single variable can be easily generated but, my concern is for 'multi variable non linear equation'.

Sir,

If I dont understand any thing wrong, you want to generate a non-linear equation using multiple variables (example: p = 5x^3 + 3y^2 - log(z) + 60), then you can use curve fitting for multiple variables (Normally curve fitting use for single variable). however,  Multi-variate ARIMA & Artificial Neural Network (ANN) are most common method for solving this type of problems. SPSS software can perform both Multi-variate ARIMA & ANN (But, it is not recommended to use SPSS for ANN). Programming language (like Matlab, R, Python) can also perform both Multi-variate ARIMA & ANN.

https://www.mathworks.com/matlabcentral/answers/75890-how-can-i-perform-multivariable-polynomial-curve-fitting

http://stackoverflow.com/questions/20769340/fitting-multivariate-curve-fit-in-python