So its been a while since I have been in college. but if water is at 255 kelvin it is probably ice.

370 kelvin is pretty close to boiling for water.

So my first question is do we need to consider a state transition and the energy required for that. if not then its a matter of ratios (as they are both water). and being honest I would just use excel to figure it out. but it would be something like

(x)(255)+(1-x)(370) = 313

comes out to x = 0.49565217

in terms of engineering - use equal portions and you should have it!!

but once again. if the 255 kelvin water is ice, then you need to calculate the energy of state transition.

good luck!