When people are upset, they access the fight/flight part of their brains.
1) Do not try to solve a problem when you or your child are upset.
2) Wait until after a cooling off period (positive time-out) when you can both access your rational brains.
3) Putting the problem on the family meeting agenda (or asking your child to) is another way to allow for a cooling off period.
This video illustrates this concept in a very memorable way.
The video talks more about how to use positive time-out as well.
If you want to learn more about the brain science underlying child development, you may want to check out this article by Melissa Healy published in the Los Angeles Times in 2009 that explains how the same lack of frontal cortex development that gives kids limited self-control is the key to their ability to learn rapidly in these early years, or this one from Parenting.com that explains the brain science behind toddler temper tantrums (take the punitive discipline advice with a grain of salt though). Another article from PBS's FRONTLINE talks about adolescent brain development and how it may influence learning and behavior.