The Brush tool family is located between the pink Eraser tool family and the Smart Brush tool family.
Many of the tools are members of tool families.
The Brush tool family has four members.
If you don't see the Brush tool icon . . .
. . . it's because one of the other family members is selected.
Press b to cycle through the four family members until the Brush tool is selected.
Or, right click on the tool family, and select the Brush tool from the menu.
The Brush tool has a blue tip (red arrow).
The Brush tool is part of a tool family.
The other members of the family are the Impressionist Brush tool and the Color Replacement tool (green box).
If you don't see the icon for the Brush tool, go to Tool Options and click on it.
The Brush tool, and many other brushes, display a circle.
Inexplicably, the circle may become a cross hairs.
Or, you not even see cross hairs.
The brush has completely disappeared.
Caps Lock is on.
Press the Caps Lock key to turn it off.
The brush is larger than your monitor.
Reduce the size of the brush.
If the above solutions didn't make the missing tool return, try the following, in the following order.
1) Save any unsaved work, close Photoshop Elements, and restart the program.
2) Restart your computer.
4) Uninstall and reinstall Photoshop Elements.
If a brush is misbehaving, check the options bar/Tool Options section.
If the opacity setting isn't at 100%, the effect of the brush is lessened.
If there's a Mode menu, open it up.
Most often, you want it to be set to Normal.
Sometimes, it's hard to see where a brush is located.
Press and hold the space bar.
The brush circle changes to the easily seen Hand tool.
Release the space bar to use the brush.