A lot of Japanese radiators also have the outlet spout soldered to the
opposite face of the tank for rigidity -- ie the spout extends across
the tank on the inside.  If the joint on the opposite side of the tank
breaks, as is usually the case if there's a leak on the outlet side,
it's far more common for the tank to be cracked than the solder joint.

You can easily tell if it's that type of construction as there'll be a
shallow semi-circular indent (to locate the spout) on the opposite
side of the tank.  It's next to impossible to identify a cracked tank
from a leaking solder joint unless you clean it up thoroughly before
making a very close visual inspection.

The only permanent fix is to remove the tank from the core, remove the
spout from the tank and repair the cracked tank with a brass plate.
The spout needs to be soldered back in, on both sides of the tank,
before the tank is replaced.  If the spout's badly rusted inside the
tank, as is often the case, you'll also need to make a new one.

Or, for a temporary repair while you're waiting for a new radiator,
silver brazing will probably last for a few days.  Soft soldering a
cracked tank would be lucky to get you once around the block.

--
John H