Well, from a theoretical standpoint, all you need to do to get the HDR-image is undo the tonemapping and exposure/camera correction.
There's many different tonemapping operators, like the common modified reinhard:
float luminance = dot(vExposedColor, float3(0.2126, 0.7152, 0.0722));
float numer = (1 + (luminance * white)) * luminance; // white = 1.0f / (whitePoint * whitePoint)
float denum = 1 + luminance;
float tonemappedLuminance = numer / denum;
return tonemappedLuminance * (vExposedColor / luminance); // => finalColor = tonemappedLuminance * (vExposedColor / luminance)
Since that outputs the final color in an HDR toolchain, you'd have to undo/reformulate that entire formula to get "vExposedColor", while choosing an appropriate whitepoint (you could make that extremely large, or use the simple reinhard instead) - input obviously is the LDR texture color. I'm not entirely sure whether this is possible, ie. if there is going to be one simple result when you undo the tonemapping operator, maybe your math is better than mine and you can see for yourself :)
Next you'd need to undo the exposure correction. If its supposed to be an image taken by a real camera, you can try to emulate that cameras parameters; alternatively you can just play around with a manual exposure constant. If you're interested in the camera-approach, the best source I have is frostbites PBR-papers, page 82:
http://www.frostbite.com/wp-content/uploads/2014/11/course_notes_moving_frostbite_to_pbr.pdf
They explain how you use simulated camera parameters for HDR/Tonemapping, so you could use those operations (computeEV100 etc... in their code samples) to calculate an appropriate exposure coefficient. EDIT: Well, you'd need to specify a manual approximation for the expected average luminance in the HDR-image in that case. There's no "simple" solution for LDR -> HDR in any way, since multiple HDR-images could result in the same LDR-image.
With that in mind, you should be able to implemented a converter; though you'd have to supply manual parameters regardless to what approach you choose, I belive.
