As sometimes occurs, my brevity and arm waving style returns to haunt me..
OK, The first one is ohms law with a bit of rounding - Adam spotted that, sums done in head tho so nearest kiloamp will do - apologies for the sloppiness!
The I2T is the adiabatic equation re-jigged for fridays.
One assumes that no heat can get out of the wire (fully lagged - adiabatic) as in the limit of an extremely short heat-up period this is true, as there is no time for heat to spread to the surrounding insulation.
Then one asks, how much energy raises the copper to boiling (for a fuse, or a 'danger temperature' for conductors where damage such as setting fire to the wallpaper becomes likely.)- this is the specific heat times the temperature rise needed, and is a certain number of joules per gram of copper. Now we need to relate the number of grams of copper per unit length of wire, to its heating. The heating is just power times pulse duration time, so I*V*T, when V is volts drop per unit length, while carrying fault current I.
Now if we pretend R per unit length is constant, and eliminate V, we get our old friend I*I*R*T = constant for any particular wire cross-section.
See the tables.
This for a fuse is the pre-arc energy - = defines the maximum current spike before parts of the fuse start to melt. (or for a given current, fixed by the substation characteristics, defines the shortest time to blow, with a zero ohm fault)
For a final circuit, one usually assumes a different final temperature (lower) and so the maximum amount of energy allowed is much less. However, for a fuse there is a second figure - the 'let through energy' in the same units, of I2T, which is the largest transient that will be ever let through to downstream devices during a fault before the fuse has finished breaking the supply.
If one wishes to cascade 2 fuses, and guarantee the thinner one only blows, under any combination of fault conditions, the pre-arc energy of the first, should be greater than the let through energy of the lighter one, so the lighter one has definitely blown clear, well before the big one reaches melting temperature. In your case it is the other way round - you want the fuse to clear before the final circuit conductors set fire to the house. However, the method is the same.
Hope that helps without being too tutorial.