That's generally not how things work. Headphones are like an extension of your ears. Your brain is always adapting the information that it receives from your ears in order to allow you to perceive a particular spectral response. If you have a particular reference recording you know well, just spend time listening to this recording through the headphones and your brain will quickly adapt to the new spectral response from the headphones.
If you are finding this process tiresome or stressful, then you probably are listening through headphones with particularly pronounced spectral peaks. This is why some headphones are easier to listen to than others. Some headphones preference the dialogue range particularly.
It is not necessary to listen to output material through an equalizer as your brain will be immediately 'equalizing' the sound upon reception. Just Listen.
Here's an example to show this in action. Take wideband pink noise and then apply a notch filter at around 1 kHz. Listen to this in your headphones for about a minute. Then immediately switch to flat full band pink noise. You will be surprised to hear a distinct tone at 1 kHz.