The standard blending equation is:
out = alpha * new + (1 - alpha) * old
old are RGB colors, and
alpha is a floating point number in the range [0,1].
So, you have (for red):
240 = 0.1 * newR + 0.9 * 255
newR, we get:
newR = (240 - 0.9 * 255) / 0.1
which evaluates to 105. Repeat for the other components, and you’re done.