Enter function,  set initial approx and tolerance

f[x_] = (E^x) - 4 + (x^2); p0 = 0. ; TOL =  .0000001;

Main algorithm (Newtons)

Print[p = p0 - f[p0]/(f')[p0]];
While[Abs[p - p0] > TOL,  
p0 = p; 
      Print[p = p0 - f[p0]/(f')[p0]]]