The heats of combustion of yellow P and red P are –9.91kJ and –8.78kJ respectively. The heat of transition of yellow to red phosphorus is

$\begin{array}{r}{\mathrm{P}}_{(\text{yellow) }}+\frac{5}{2}{\mathrm{O}}_2\left(\mathrm{g}\right)⟶\frac{1}{2}{\mathrm{P}}_2{\mathrm{O}}_5\left(\mathrm{s}\right);{\mathrm{\Delta H}}_1=-9.91\mathrm{kJ}\\ {\mathrm{P}}_{\left(\text{red }\right)}+\frac{5}{2}{\mathrm{O}}_2\left(\mathrm{g}\right)⟶\frac{1}{2}{\mathrm{P}}_2{\mathrm{O}}_5\left(\mathrm{s}\right);{\mathrm{\Delta H}}_2=-8.78\mathrm{kJ}\end{array}$
Rearranging, we get
$\begin{array}{l}{\mathrm{P}}_{(\text{yellow) }}+\frac{5}{2}{\mathrm{O}}_2\left(\mathrm{g}\right)⟶{\mathrm{P}}_2{\mathrm{O}}_5\left(\mathrm{g}\right);\mathrm{\Delta H}=-9.91\mathrm{kJ}\\ {\mathrm{P}}_2{\mathrm{O}}_5⟶{\mathrm{P}}_{\text{(red) }}+\frac{5}{2}{\mathrm{O}}_2\left(\mathrm{g}\right);\mathrm{\Delta H}=+8.78\mathrm{kJ}\end{array}$
Adding these two equations, we get
${\mathrm{P}}_{\left(\text{yellow }\right)}⟶{\mathrm{P}}_{\left(\text{red }\right)};(-9.91+8.78)\mathrm{kJ}=-1.13\mathrm{kJ}$