For images with very high contrast sometimes it is necessary to boost the mid-tones to balance the image. To do this in GIMP or Photoshop, set three points on the tone curve at roughly equal positions along the curve, and then move the middle one upwards to achieve the effect. The other two points act as anchors, keeping the shadows and highlights unchanged. The moving the mid-point downwards has the opposite effect, and can help with very low contrast images.
In Photoshop Elements this is much easier to achieve. From the default setting, simply move the slider for Midtone Brightness up or down to produce the desired effect.
That's quite enough maths homework for one week, but next week I'll look at more extreme Curves effects, including Solarisation, Posterisation and Tone Reversal.