System Information
Operating system: Windows-10-10.0.18362-SP0 64 Bits
Graphics card: AMD Radeon(TM) R3 Graphics ATI Technologies Inc. 4.5.13558 Core Profile Context 26.20.11008.1007

Blender Version
Broken: version: 2.83.2, branch: master, commit date: 2020-07-09 05:50, hash: rB239fbf7d936f
Worked: has not worked in any previous version tried

Short description of error
The boolean modifier with a difference operation in some cases adds the meshes instead of subtracting them.

This problem may occur in part because of a mirroring of some vertices in the mesh on which the modifier is added.

I have seen this problem in numerous versions of Blender (2.83.2, 2.79b, 2.76b), running on numerous different systems.

Here is a StackExchange issue I made a while ago (with screenshots). I had thought that a different solver resolved the issue, but it still persists even in more recent versions.

https://blender.stackexchange.com/questions/160711/why-does-boolean-difference-add-material-to-this-mesh

I have tried editing the meshes involved, using different modifiers, and other approaches. So far, I have not managed to find a way to fix or work around this issue.

Exact steps for others to reproduce the error

In the attached file, the mesh "Cylinder.001.Frame" has two active meshes that should show difference modifiers. The one with the mesh "Text.Version.002.3-4mm.goggles1.001" adds material instead of subtracting it.