This can be done with css masking, though unfortunately browser support is really bad (I believe webkit only).
http://jsfiddle.net/uw1mu81k/1/
-webkit-mask-box-image: url(http://yourimagehere);
Because your image is all white, it is a perfect candidate for masking. The way the mask works is that wherever the image is white, the original element is shown as normal, where black (or transparent) the original element is not shown. Anything in the middle has some level of transparency.
EDIT:
You can also get this to work in FireFox with slight help from svg
.
http://jsfiddle.net/uw1mu81k/4/
div {
width: 50px;
height: 50px;
mask: url(#mymask);
-webkit-mask-box-image: url(http://www.clker.com/cliparts/F/5/I/M/f/U/running-icon-white-on-transparent-background-md.png);
}
<div style="background-color: red;"></div>
<div style="background-color: blue;"></div>
<div style="background-color: green;"></div>
<div style="background-color: orange;"></div>
<div style="background-color: purple;"></div>
<svg height="0" width="0">
<mask id="mymask">
<image id="img" xlink:href="http://www.clker.com/cliparts/F/5/I/M/f/U/running-icon-white-on-transparent-background-md.png" x="0" y="0" height="50px" width="50px" />
</mask>
</svg>
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