ok not sure i understand you correctly but here goes,

( i did  this with you second image, but will also work with your first)

take you image into photoshop, then duplicate layer in the layer panel (you need to do this to be able to activate the layer style options), hide the underlying layer (make non- visible) and select the duplicate layer,

then click "layer" (drop down-menu) then select "layer style", then "blending options...",
now you have your layer style popup window, at the bottom you'll see two sliders, one says "this layer" it has a black end slider and a white end slider, if you click and drag on the white end slider from right to left (doesn't have to move very much at all),

you will now have no white visible, and be left with a transparent background replacing that which was white, save that as a .png, problem solved, you now have a transparent image again.

(puts super-hero cape back on, and assumes his heroic pose, again Vince has saved the day, starts to mumble something about he doesn't do it for the fame but for his fellow... blah, blah)