Pre-tax cash flow is calculated by adding rents, other operating income, and gains on the sale of a property, then subtracting operating expenses like maintenance or paying a property manager, as well as property taxes and mortgage payments.
Invested equity is simply the amount of cash the investor brought to closing.
It's worth pointing out that cash-on-cash return only looks at invested equity, so it's a leveraged metric. That differs from a metric like capitalization rate (cap rate), which uses the property's entire value to calculate returns.