So this isn't impossible, but will be somewhat hard to achieve.
Telephone modem code base will not be immediately useable because it is designed for 8-bit nonlinear quantization, sampled at 8 kHz and a single pair of wires for both directions.
The typical audio line-in/line-out ports would support 48kHz sampling, 16-bit linear quantization and a separate wires for each direction.
Maybe this board is read by a telecommunication student who may have SDSL modem source code handy and be willing to downrate such a code to 20kHz audio band and is not bound by 3rd party licensing requirements.
Two possible ways forward:
1) try to integrate some amateur radio code like http://en.wikipedia.org/wiki/WSJT_(Amateur_radio_software) . There are several people here who could advise you how to modify it to take advantage of wider bandwidth, much better signal/noise ratio and no multipath/echo.
2) see if you can write on your own a code to generate a 10kHz sine wave and a code to receive it properly at -3dB with AGC (automatic gain control). If you manage that then again this board has enough people familiar with amateur radio to advise you how to implement simple QAM channel (Quadrature-Amplitude Modulation). It shouldn't be that hard to reach somewhere between 1/10 and 1/3 of the bandwidth you originally asked for.
In my humble opinion the most work will be related to integration, not actual DSP. Things like: which of the several standards of audio drivers to use; how to detect available drivers; how to control output volume to avoid distortion; how to control input volume to avoid both noise and distortion. And last but not least: how to disable various sound effects, pseudo-3D audio, super-bass, etc.