Calculate Z score by a given P value

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I want to find the Z-score by a given P-value. Usualy what I do is finding it in a Z-TABLE, one of many which I find on google. But, I want to write an algorithm (in code) so I can calculate that value by myself in one click without using the table. I have searched alot and all I found is that formula: $$ Z=\frac{x-\mu}{\sigma} $$ But as I said I want to calculate the z-score by p-value only. I will very much appreciate your help finding a solution :)