Two issues here. First you aren't taxed on your gross income, at the minimum you'd typically reduce your gross income by the standard deduction (12,550 for single (not if married filing single, and not if you're a nonresident alien/dual status alien barring certain exceptions).
Second, the highest tax rate does not apply to all your taxable income, but only the amount of taxable income in the associated bracket. So you won't pay 24% or 32% on all of your taxable income, just a portion, and you'll pay a lower rate on other portions of your income. This bracket makes it easy as it calculates the total tax-owed for all prior brackets:
Assuming you only take the standard deduction and no other adjustments, your taxable income would be either 153,000 - 12,550 = 140,450 or 175,000 - 12,550 = 162,450
Your top marginal rate would be 24% bracket for either, so the difference in tax paid would just be 24% of the difference in base pay. If the top marginal rate were in different brackets you'd just have to do the math for the tax-owed column to compare.