Quality Of Earnings Report

As noted by Mr. Frey, there is no standard for a quality of earnings report.
I associate this terminology with the lower middle market PE firms. In the middle market and above, PE firms generally engage CPA firms or consultants to perform "financial due diligence." In the lower middle market, the PE firms frequently ask for "Quality of Earnings" reports which are, presumably, more limited in scope and lower in cost. Normally, the PE firm would engage its own advisors to provide them with this report, based on analysis of the company's financial information, policies, etc.
The question suggests, however, that the PE firm is still in the early stages and is looking for more information directly from the company. Their focus is likely to be on EBITDA, normalized to exclude nonrecurring items and costs that will be eliminated or reduced as part of the proposed transaction (excess compensation to owners, etc.).
The best thing you can do is to ask them what they are looking for, then deliver exactly what they need.

Both Bryan and Stephen are correct that each quality of earnings is unique to the company. I worked with EY Transaction Advisory Services, where we prepared QofE schedules during our due diligence projects for private equity firms. Since leaving EY, I joined a PE firm where we requested this analysis when we were buying a company as well as when we were positioning a company to be sold. Recently, I started a consulting firm that provides financial due diligence and other corporate advisory services.

A typical QofE schedule begins with reported EBITDA for the last few years, the recent trailing twelve months, and the two comparative stub periods. It's important to list each adjustment (as described by Bryan & Stephen), footnote accordingly as to why it should be an adjustment to reported EBITDA, then ultimately present the Adjusted EBITDA or Pro forma EBITDA.

Pick a P&L format and periods that you think are relevant and can tie back to your audited (I assume) financials and highlight any unusual items line by line. One off sales, sales of excess or obsolete inventory, unusual charges, atypical promotions etc.... It may be interesting to look at your corporate tax return (assuming you're a C corp) and the reconciliation between tax and book earnings to see if anything jumps out at you as unusual. If you have a spare weekend, get Thronton L. O'glove's book Quality of Earnings. It's an interesting read and my help bring out items you wouldn't have considered. Enjoy.

There are templates for such a summary of earnings that I have used and/or developed over the years. Typically these QofE templates are very similar among Big 4 advisors who prepare them. If the VC/PE firm is looking to acquire a company, the QofE will also (or should also) include a distinct analysis of owner 'add-backs'. While every company has its nuances, the VC/PE acquirer tends to normalize performance metrics used across its portfolios and so some of the standard earnings measurements (and the underlying detail and commentary) are often generically applied in a QofE analysis.

I have examples if required.

Courtesy of Tony Enlow. https://www.proformative.com/og/resource/general-content/quality-earnings-presentation. Enjoy!

I have never used a QofE template. It has always been different things in different situations. The goal of a QofE is for PE firms to catch strange items in your financials before they take a closer look. You may start with EBITDA for the last few years. Also show them cash flows. If they come back with more questions, find out what exactly they would like to see.