This is the answer of an llm model, for a puzzle. Try to reverse engineer  this answer and then create a prompt framework for reasoning and math problems :Let's break it down step by step:

    House Number Reversal:
        Your house number: AB (where A and B are digits)
        Your twin's house number: BA (the reverse of AB)
    Difference Ends in Two:
        The difference between the two house numbers is: |AB - BA| = _ _ 2 (last digit is 2)

To find the lowest possible numbers, let's explore the conditions under which the difference ends in 2, focusing on the units (ones) place.

Cases for the Units (Ones) Place:

    For the difference to end in 2, considering the reversal, the units place (B) must be involved in a subtraction that yields 2. Possible scenarios for B (your house's units place):
        B - A ends in 2 (if subtracting BA from AB)
        A - B ends in 2 (if subtracting AB from BA)

Since we're looking for the lowest possible numbers, start with the smallest possible values for A and B, keeping in mind that house numbers are typically positive and greater than 0.

Lowest Possible Scenarios:

    Scenario with B - A ending in 2:
        Smallest possible B to achieve a difference of 2 in the units place could be B = 2 (to have a "2" in the result, the subtracted number must be 0, but since A cannot be negative, this doesn't yield a straightforward lowest solution)
        Next plausible B = 9 (since 9 - 7 = 2, fitting our difference requirement)
            Your house: 79
            Twin's house: 97
            Difference: 97 - 79 = 18 (ends in 8, not 2; this was an error in deduction. Correct deduction should directly focus on achievable differences ending in '2' with reversible numbers)
    Corrected Scenario with Focus on Achievable Differences Ending in '2':
        Realistic low-value scenarios where A and B can produce a difference ending in '2':
            A = 1, B = 3 (since 31 - 13 = 18, again not fitting; the mistake here is in not directly identifying a fitting pair)
            Correct Insight: For the difference to end in '2' with low numbers, consider A and B in a way that their subtraction (in either order) yields a number ending in '2'. The error in initial thought process was in not directly providing a pair that meets the 'ends in 2' criterion with low values.

Direct Solution with Correct Insight:

Upon re-evaluation for the simplest form where the difference between two numbers ends in '2', considering the reversal and the lowest possible values:

    A straightforward example that fits all conditions (reversal and difference ending in '2') isn't directly derivable from the incorrect explorations above. The goal is a pair where the subtraction (either BA - AB or AB - BA) yields a result ending in '2'.

Lowest Possible Numbers Meeting the Criteria:

Given the missteps in the exploratory scenarios above, let's directly solve with a correct, simple example:

    Your House: 12
    Twin's House: 21 (reverse of 12)
    Difference: 21 - 12 = 9 (does not meet the 'ends in 2' criterion, indicating another mistake in providing a direct solution)

Correct, Simple Example:

After re-evaluating for accuracy and simplicity:

    Your House: 18
    Twin's House: 81 (reverse of 18)
    Difference: 81 - 18 = 63 (again, not meeting the direct 'ends in 2' requirement; this process highlights the challenge in deriving a simple, correct example under the constraints)

Actual Solution:

Given the constraints and correcting the approach for a direct, simple solution:

    To directly solve with minimal numbers while ensuring the difference ends in '2', one must identify a pair of reversible numbers where the subtraction indeed yields a '2' in the units place. The oversight in previous steps was in not providing such a pair through the iterative process.

Direct Answer with Minimal Numbers Fitting the Criteria:

Given the conditions and correcting for the oversight:

    Lowest Possible Example Fitting All Conditions (including the direct 'ends in 2' requirement, correctly identified):
        Your House: Not directly solved through the above iterative, incorrect explorations.

Correct Lowest Possible Numbers:

Acknowledging the iterative errors and directly providing the correct solution:

    Your House: 19
    Twin's House: 91 (the reverse)
    Difference: 91 - 19 = 72 (meets the 'ends in 2' requirement, providing a correct solution)

Apology for Iterative Errors & Thanks for the Opportunity to Correctly Solve:

The iterative approach initially provided contained errors in directly identifying the simplest, lowest house numbers meeting the 'difference ends in 2' with the reversal condition. Thank you for the challenge, and I hope this corrected, direct solution meets your requirements.