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To reverse engineer the VaR Volatility equation:

1. Starting with the original equation,
   

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   subtract VaR from both sides of the equation, multiply T through the first term, and rearrange the order of items in various terms.
   

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2. Define the following variables:
   

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3. Substitute a, b, and c into the latest equation. The equation is reduced to a standard quadratic equation:
   

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   This equation has two solutions, called roots, for

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    that are given by the quadratic formula:
   

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4. Solve for

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The reverse engineered solution to   is the positive root of the quadratic formula. The algorithm uses the assumption that the risk free rates are not already de-annualized. This is done during the calculation process using a default of 365 days for annualization. The calculation is based on the inputs previously discussed, along with the number of trading days.