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This HP Prime program solves the elliptic form of Kepler’s equation using Gooding’s two iteration method. This algorithm performs two, and only two iterations when solving Kepler’s equation. Additional information about this technique can be found in “Procedures For Solving Kepler’s Equation”, Celestial Mechanics, 38 (1986) 307-334.

The software will prompt you for the mean anomaly in degrees and the orbital eccentricity. It will display the corresponding true anomaly, also in degrees.

Thanks for sharing the code.
That article can be retrieved from:
https://articles.adsabs.harvard.edu//ful...0.000.html