inverse function of Tetens formula

tetens_inv.rb

def tetens t
  6.112 * Math.exp(17.67 * (t - 273.15) / (t - 29.65))
end

def invtetens e
  k = Math.log(e/6.112) / 17.67
  0.05 * (-5463.0 + 593.0 * k) / (-1.0 + k)
end

(0..50).each {|tc|
  t = tc + 273.15
  e = tetens(t)
  rt = invtetens(e)
  rtc = rt - 273.15
  printf "%10.2f %10.2f %10.2f\n", tc, e, rtc
}